DATE : 24-04-16 VIBRANT ACADEMY

REVIEW TEST–1 (MEGA PHASE-I COURSE-2017)JEE Mains

Time : 3 Hours Maximum Marks : 360Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.

INSTRUCTIONSA. General :

1. This booklet is your Question Paper containing 90 questions. The booklet has32 pages.

2. The question paper CODE is printed on the right hand top corner of this sheet andon the back page (page no. 32) of this booklet.

3. The question paper contains 3 blank pages for your rough work. No additional sheetswill be provided for rough work.

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5. Fill in the boxes provided below on this page and also write your Name and VARoll No. in the space provided on the back page (page no. 32) of this booklet.

6. The answer sheet, a machine-readable Objective Response Sheet (ORS), is providedseparately.

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8. Do not open the question-paper booklet before being instructed to do so by the invigilators.

B. Question paper format Read the instructions printed on the back page

C. Marking scheme (page no. 32) of this booklet.

Name of the candidate VA Roll Number

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.......................................................... ............................................................ Signature of the Candidate Signature of the invigilator

VIBRANT ACADEMY(India) Private Limited

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CODE - A

USEFUL DATAAtomic weights: H = 1, He = 4, Li = 7, g = 10 m/s2 , B = 11, C = 12, N = 14, O = 16, F = 19, Ne = 20, Na = 23,Mg = 24, Al = 27, P = 31, S = 32, Cl = 35.5, K = 39, Ca = 40, Ar = 40 , Ti = 48, Cr = 52, Mn = 55, Fe = 56,Co = 59, Cu = 63.5, Zn = 65.5, Br = 80, Mo = 96, Ag = 108, I = 127, Ba = 137, U = 238

DATE : 24-04-16

Vibrant Academy (I) Pvt. Ltd. "A-14(A)" Road No.1, Indraprastha Industrial Area, Kota (Raj.) Ph. 0744-2423406 [RT-1,JM-A-2]

PART I : MATHEMATICSSingle Correct Choice Type

This section contains 30 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for itsanswer, out of which ONLY ONE is correct.

1. Let a, b R, (a 0). If the function f defined as

2

2

3

2x , 0 x 1a

f(x) a , 1 x 2

2b 4b , 2 xx

is continuous in the interval

[0, ), then an ordered pair (a, b) is :

(A) 2,1 3 (B) 2,1 3 (C) 2, 1 3 (D) 2,1 3

2. Let a1, a2, a3,....,an,.... be in A.P. If a3 + a7 + a11 + a15 = 72, then the sum of its first 17 terms is equal to

(A) 153 (B) 306 (C) 612 (D) 204

3. If n 2

6n 2

2

C11

P

, then n satisfies the equation :

(A) n2 + n – 110 = 0 (B) n2 + 5n – 84 = 0 (C) n2 + 3n – 108 = 0 (D) n2 + 2n – 80 = 0

Space For Rough Work



MATHEMATICS

4. If the coefficients of x–2 and x–4 in the expansion of

1813

13

1x

2x

, (x > 0), are m and n respectively, then mn

is equal to

(A) 54

(B) 45 (C) 27 (D) 182

5. If x is a solution of the equation, 12x 1 2x 1 1, x2

, then 24x 1 is equal to

(A) 2 (B) 34

(C) 2 2 (D) 12

6. If quadratic equations x2 + x + 1 = 0 and (b – c)x2 + (c – a)x + (a – b) = 0 have both the roots common,then is :

(A) –3 (B) – 2 (C) – 1 (D) 1

7. A circle passes through (– 2, 4) and touches the y-axis at (0, 2). Which one of the following equations canrepresent a diameter of this circle?(A) 2x – 3y + 10 = 0 (B) 3x + 4y – 3 = 0 (C) 4x + 5y – 6 = 0 (D) 5x + 2y + 4 = 0



MATHEMATICS

8. If a variable line drawn through the intersection of the lines x y 13 4 and

x y 14 3 , meets the coordinate

axes at A and B, (A B), then the locus of the midpoint of AB is(A) 7xy = 6(x + y) (B) 4(x + y)2 – 28(x+ y) + 49 = 0(C) 6xy = 7(x + y) (D) 14(x + y)2 – 97(x + y) + 168 = 0

9. If f(x) is differentiable function such that f'(2) = 6, f'(1) = 4 and k9

)1(f–)1h2–h2(f)2(f–)2h3h(flim 2

3

0h

then k =

(A) 1 (B) 2 (C) 3 (D) 4

10. The value of 1515

2 r15

r 1 r 1

Cr

C

is equal to

(A) 1240 (B) 560 (C) 1085 (D) 680

11. The point (2, 1) is translated parallel to the line L : x – y = 4 by 2 3 units. If the new point Q lies in the third

quadrant, then the equation of the line passing through Q and perpendicular to L is

(A) x + y = 2 6 (B) 2x + 2y = 1 6 (C) x + y = 3 3 6 (D) x + y = 3 2 6



MATHEMATICS

12. For x R, x 0, x 1 let f0(x) = 1

1 x and fn + 1(x) = f0(fn(x)), n = 0, 1, 2, ....... Then the value of

100 1 22 3f (3) f f3 2

is equal to

(A) 83 (B)

43 (C)

53 (D) 1

3

13. If the function 1

x, x 1f(x)

a cos (x b), 1 x 2

is differentiable at x = 1, then ab is equal to

(A) 2

2

(B) 2

2

(C) 2

2

(D) – 1 – cos–1(2)

14. If 2x

32x

a 4lim 1 e ,x x

then 'a' is equal to

(A) 2 (B) 32

(C) 12

(D) 23

15. Let x, y, z be positive real numbers such that x + y + z = 12 and x3y4z5 = (0.1) (600)3. Thenx3 + y3 + z3 is equal to(A) 342 (B) 216 (C) 258 (D) 270



MATHEMATICS

16. The number of distinct real roots of the equation, cosx sinx sinxsinx cos x sinx 0sinx sinx cosx

in the interval ,4 4

is

(A) 1 (B) 4 (C) 2 (D) 3

17. For x R, x –1, if

(1 + x)2016 + x(1 + x)2015 + x2(1 + x)2014 + ...... + x2016 = 2016

ii

i 0a x

, then a17 is equal to

(A) 2017!

17! 2000! (B) 2016!

17! 1999! (C) 2016!16! (D)

2017!2000!

18. If the four letter words (need not be meaningful) are to be formed using the letters from the word"MEDITERRANEAN" such that the first letter is R and the fourth letter is E, then the total number of all suchwords is

(A) 110 (B) 59 (C) 311!

(2!) (D) 56

19. The value of 11 1cos cos2 8

is equal to

(A) 3/4 (B) – 3/4 (C) 1/16 (D) 1/4



MATHEMATICS

20. The graph of the function 2af(x) log x x 1

is symmetric about

(A) x-axis (B) Origin (C) y-axis (D) the line y = x

21. Let f(x) = log2(|sinx| + |cosx|). The range of f(x) is(A) [– 1, 0] (B) [0, 1/2] (C) [– 1/2, 0] (D) [0, 1]

22. 2x 0

xcosx log(1 x)limx

is equal to

(A) 1/2 (B) 0 (C) 1 (D) None of these

23.

|x|

xsin)e–1(lim x0x

is equal to

(where [·] denotes G.I.F)(A) 0 (B) 1 (C) –1 (D) Does not exist


MATHEMATICS


24. Number of points of discontinuity of the function y = f(f(x)) where nx1)x(f

in (1, ) is

(A) 1 (B) 2 (C) 3 (D) 0

25. Number of value(s) of 'x' satisfying 5{x} = x + [x] and [x] – {x} = 21

is/are

(where [·] denotes G.I.F. and {·} denotes fractional part function)(A) 0 (B) 1 (C) 2 (D) More than 2

26. If )x3(tan22

–x91

x6cos 1–2

1–

then complete set of values of 'x' is

(A) (–1, 1) (B) 1,3

(C)

31,

31–

(D) None of these

27.x–11–

1x 2xeccoslim

is equal to

(where [·] denotes greatest integer function)(A) 0 (B) 1 (C) (D) Does not exist



MATHEMATICS

28. Let x x

2a a 2f(x)

x

x > 0 (a > 0)

= 3ln(a – x) – 2 x 0if f(x) is continuous at x = 0, then 'a' can be

(A) 1 (B) e (C) 1e (D) 2e

29. Let f(x) = max.{cosx, x, 2x – 1} where x 0, then number of point(s) of non-differentiability of f(x) is/are(A) 1 (B) 0 (C) 2 (D) More than 2

30. Which of the following quantity is negative?(A) tan–1(tan4) (B) cot–1(cot4) (C) tan(cos–1(cos5)) (D) cot(sin–1(sin4))


PART II : PHYSICSSingle Correct Choice Type


31. In the figure, mass of A = 2 kg and mass of B = 4 kg. For what minimum value of force F, block A startsslipping over block B.

(A) 24 N (B) 36 N (C) 12 N (D) 20 N

32. Two blocks of masses m and M are joined with an ideal spring of spring constant k and kept on a roughsurface as shown. The spring is initially unstretched and the coefficient of friction between the blocks and thehorizontal surface is . What should be the maximum speed of the block of mass M such that the smallerblock does not move?

m M

v0

k

(A) Mmg

M m k

(B) (M m)kg

Mm

(C) (2M m)kg

kM

(D) None of these

33. Force acting on a block moving along x-axis is given by

F = – 2

4x 2

Newton

The block is displaced from x = – 2m to x = + 4m, the work done will be(A) positive (B) negative (C) zero (D) Information insufficient



PHYSICS


34. A glass dumbbell of length 50 cm and refractive index 1.5 has ends of 5 cm radius of curvature. A point objectis situated in air at a distance of 20 cm from the end P of the dumbbell along the axis. Find the distance(from P) of image due to refraction at surface of P only.

=1.5

5cm

P

(A) 30 cm (B) 15 cm (C) 10 cm (D) 5 cm

35. A graph is plotted with PV/T on y-axis and mass of the gas along x-axis for different gases. The graph is :(A) a straight line parallel to x-axis for all the gases(B) a straight line passing through origin with a slope having a constant for all the gases.(C) a straight line passing through origin with a slope having different values for different gases(D) a straight line parallel to y-axis for all the gases.

36. A cylinder of ideal gas is closed by an 8.00 kg movable piston (area = 60 cm2) as shown in figure. Atmo-spheric pressure is 100 kPa. When the gas is heated from 30.0°C to 100.0°C, the piston rises 20.0 cm. Thepiston is then fastened in place, and the gas is cooled back to 30.0°C. If Q1 is the heat added to the gas inthe heating process, and Q2 is the heat lost during cooling find the difference |Q1| – |Q2| is.

Piston

Gas

(A) 32.5 cal (B) 30.0 cal (C) 28.5 cal (D) 20.0 cal


PHYSICS


37. The focal lengths of the objective and the eye-piece of a compound microscope are 2.0 cm and 3.0 cm,respectively. The distance between the objective and the eye-piece is 15.0 cm. The final image formed by theeye-piece is at infinity. The two lenses are thin. The distance (in cm) of the object and the image produced bythe objective, measured from the objective lens, are respectively.(A) 2.4 and 12.0 (B) 2.4 and 15.0 (C) 4.2 and 12.0 (D) 4.2 and 3.0

38. A particle of mass m oscillates along APB (speeds zero at A & B) inside a smooth spherical shell of radiusR. At any instant the kinetic energy of the particle is K. Then the force applied by particle on the shell at thisinstant is

(A) RK

(B) KR2

P

BAg

(C) RK3

(D) R2K

39. A hydrogen cylinder is designed to withstand an internal pressure of 100 atmospheres. At 27°C the hydrogenpumped into the cylinder exerts a pressure of 20 atmospheres. At what temperature does the danger ofexplosion first set in ?(A) 1200°C (B) 1227°C (C) 1300°C (D) 1327°C

40. A hollow double concave lens is made of very thin transparent material. It can be filled with air or either of twoliquids L1 or L2 having refractive indices 1 and 2 respectively. (2 > 1 > 1). The lens will diverge a parallelbeam of light if it is filled with(A) air and placed in air (B) air and immersed in L1

(C) L1 and immersed in L2 (D) L2 and immersed in L1


PHYSICS


41. A concave spherical mirror forms a real magnified image of an object which is twice as big as the object.However, if the object is moved by 15 cm away from the mirror the magnification becomes – 1. If the objectis moved further by another 15 cm, the magnification will now be(A) – 0.67 (B) – 1.25 (C) – 0.33 (D) –1.33

42. Three particles A, B and C are projected with initial velocities vA, vB and vC (in vertical plane) as shown infigure. The particles collide at highest point of A. Then vA : vB : vC is :

(A) 21:1:

23

(B) 1:1:3 (C) 3:23:1 (D) None

43. A 2 kg block is gently pushed from rest at A and it slides down along the fixed smooth circular surface. If theattached spring has a force constant k = 20 N/m. What is unstretched length of spring so that it does notallow the block to leave the surface until angle with the vertical is = 60°?

(A) 1m (B) 1.5 m (C) 0.5 m (D) 0.8 m


PHYSICS


44. An ideal gas is initially at a temperature T and volume V. Its volume is increased by V due to an increase in

temperature T, pressure remains constant. The quantity TV

V

varies with temperature as :

(A) (B) (C) (D)

45. A small straight rod is placed at an inclination with the optical axis of a thin lens as shown in the figure. Thebase of the rod is on the optical axis and at a distance 2f(f = focal length of the lens) from the lens.The image of the rod would be like :

2f

(A) (B) (C) (D)

46. A light ray is incident perpendicular to one face of a 90° prism and is total internally reflectd at the glass-airinterface. If the angle of reflection is 45°, we conclude that (the refractive index of glass is n).

(A) 3n

2 2 (B) n >

32 2

(C) n < 3

24 (D) None


PHYSICS


47. The image formed by an objective of a compound microscope is(A) virtual and diminished (B) real and diminished(C) real and enlarged (D) virtual and enlarged

48. Different forces are applied to each of four 1 kg blocks to slide them across a surface at constant speed asshown. In which diagram is the coefficient of friction between the block and the steel smallest ?

(A) (B)

(C) (D)

49. The string between blocks of mass m and 2m is massless and inextensible.The system is suspended by a massless spring and is in equilibrium asshown. If the string is cut find the magnitudes of accelerations of mass 2mand m (immediately after cutting)

(A) g, g (B) g, 2g

(C) g,2g

(D) 2g,

2g


PHYSICS


50. Half part of the rear surface of a thin equiconvex lens of focal length 40 cm and refractive index 1.5 is silvered.If parallel rays are incident on this lens, then the distance between the two images.

(A) 50 cm (B) cm3

80

(C) 40 cm (D) None

51. A mango tree is at the bank of river and one of the branch of tree extends over the river. A tortoise lives insideriver. A mango falls just above the tortoise. The acceleration of the mango falling from tree appearing to thetortoise is (Refractive index of water is 4/3 and the tortoise is stationary)(A) g (B) 3g/4 (C) 4g/3 (D) None of these

52. Convex surface of thin concavo - convex lens of refractive index 1.5 is silvered as shown. A small object iskept in air at 30 cm left of the lens on its principal axis. the distance of the final image from mirror is

(A) 20 cm (B) 30 cm (C) 10 cm (D) 15 cm


PHYSICS


53. In the following P-V diagram of an ideal gas, two adiabates cut two isotherms at T1 = 300K and T2 = 200K.The value of VB/VC

P

V

CD

AB AB T 1

DC T 2

VA VD VB VC

(A) = VA/VD (B) < VA/VD (C) > VA/VD (D) 3/2

54. The kinetic energy (KE) vs time graph for a particle moving along a straight line is shown in the figure.

The force vs time graph for the particle may be

(A) (B)

F

(C) (D)



PHYSICS55. A point on P-V diagram represents :

(A) The state of a system (B) Work done or by a system(C) Work done in a cyclic process (D) A thermodynamic process

56. For the system shown in the figure, the tension in the string is T. The tension will become 2T by addingmass_______on______.

MA

2M B

(A) 2M, B (B) 4M, B (C) 2M, A (D) 3M, A

57. A long solid cylinder is radiating power. It is remoulded into a number of thinner cylinders, each of which hasthe same length as original cylinder. Each thin cylinder has the same temperature as the original cylinder.The total radiant power emitted by the pieces is twice that emitted by the original cylinder. How many smallercylinders are there ? Neglect the energy emitted by the flat faces of cylinder.(A) 3 (B) 4 (C) 5 (D) 6


58. In the isothermal expansion of an ideal gas (Choose the INCORRECT option) :(A) there is no change in the temperature of the gas(B) there is no change in the internal energy of the gas(C) the work done by the gas is equal to the heat supplied to the gas(D) the work done by the gas is equal to the change in its internal energy

59. Two coherent monochromatic light beams of intensities I and 4I are superposed. The maximum and mini-mum possible intensities in the resulting beam are(A) 5I and I (B) 5I and 3I (C) 9I and I (D) 9I and 3I

60. In a two-slit experiment, with monochromatic light, fringes are obtained on a screen placed at some distancefrom the slits. If the screen is moved by 5 × 10–2m towards the slits, the change in fringe width is 10–3m. Thenthe wavelength of light used is (given that distance between the slits is 0.03 mm)(A) 4000 Å (B) 4500 Å (C) 5000 Å (D) 6000 Å


PHYSICS


PART III : CHEMISTRYSingle Correct Choice Type


61. A solution contains two cations Ba2+ and Pb2+ along with common anion, this common anion is(A) Cl– (B) S2– (C) CH3COO– (D) CrO4

2–

62. How many number of fractions are obtained on fractional distillation of products in below reaction?

CH3

CH

H ClCl2h

CH3H3C(S)-2-Chloro-3-methylbutane

Dichloro Products (Including stereoisomers)

(A) 3 (B) 4 (C) 5 (D) 6

63. SO bond energy in SO2 molecule is greater than OO bond energy in O3 molecule, correct set of structure ofSO2 and O3 molecules is

(A) S..

OOO..

OO(B)

S..

OOO..

OO

(C) S..

OOO..

OO(D) S

..

OOO..

OO




CHEMISTRY64. X + Y XY Rate = k[X]p[Y]q

Initial conc. [X] Initial conc.[Y] Rate (mol litre–1 second–1)0.2 M 0.2 M 0.050.1 M 0.2 M 0.0250.2 M 0.4 M 0.10The value of p and q are :(A) p = 1 q = 1 (B) p = 2 q = 0 (C) p = 2 q = 1 (D) p = 2 q = 2

65. In which of the following major product is INCORRECT

(A) H2

Pd-BaSO4

(B)

CH3

Ph

C–Cl

O

HH –Pd2

BaSO4

CH3

Ph

C–H

O

H

(C) H –1eq.2

Pd

(D) H2

Pd-BaSO4

O OH

66. Which of the following has strongest H-bond.

(A) :N H — F (B) :O H O H

:

(C) :O H — F

:

(D) :N HO

H



CHEMISTRY67. Given A(g) 2B(g) concentration of A are in arithmatical progression in equal interval of time. Which is

correct statement about this reaction ?

(A)

time

=degree ofdissociation of A

1.0

(B)

time

Rate offormation

of B

(C)

time

Conc.ofA

(D)

time

Rate ofconsumption

of A

68.

cold.dil KMnO4

Br /CCl2 4

(X) Number of products (including stereoisomers)

(Y)Number of products (including stereoisomers)

Sum of (X) + (Y) is :(A) 2 (B) 3 (C) 4 (D) 5

69. Energy distance relationship between HCl - - - HCl and HF ---- HF in solid state is respectively.

(A) 3r1

, 3r1

(B) 3r1

, 4r1

(C) 4r1

, 3r1

(D) 4r1

, 4r1


CHEMISTRY


70. Which is incorrect statement about real gas ?(A) Boyle temperature is greater than critical temperature.(B) At Boyle temperature second virial coefficient of a gas is zero(C) At critical point, attractive force dominate to repulsive force.(D) At critical point repulsive force and attractive force balance to each other.

71. What is the final major product P of the following reaction sequence?

CHH C2 CH

CH2 Br2 D2 / PdP

(A)

CH – Br2

HH

BrD

CH – D2

(B)

CH – Br2

HH

DD

CH – Br2

(C)

CH –Br2

HD

DH

CH Br2–

(D)

CH – D2

HBr

BrH

CH – D2

72. A 100 ml mixture of NaOH and Na2CO3 required 100 ml 0.2 M HCl using phenolphthalein as indicator but 50ml of same mixture required 75 ml 0.2 M HCl when methyl orange was used as indicator the molar ratio ofNaOH and Na2CO3 in the mixture was.(A) 1 : 1 (B) 1 : 2 (C) 2 : 1 (D) 2 : 3

73. Hybrid orbitals of which central atom have least percentage s-character in their bonds :(A) P(SiH3)3 (B) N(SiH3)3 (C) Triplet Carbene (D) O(SiH3)2


74. P mole of KHC2O4.3H2C2O4 is oxidised completely by 400 ml 1.0 M KMnO4 in acidic medium and Q moleof KHC2O4.H2C2O4 is neutralised completely by 300 ml 1.0 M of Ca(OH)2 then the ratio of P and Q is :(A) 5 : 4 (B) 5 : 2 (C) 10 : 3 (D) 8 : 3

75. Major product of the following reaction is

HBrCCl4

?

(A)

Br

(B) Br (C) Br

(D)

Br

76. Element X is an alkaline earth metal, X forms an insoluble carbonate and more soluble than strontiumhydroxide, element 'X' is(A) Calcium (B) Barium (C) Sodium (D) Caesium

77.

Hg(OAc) ,H O2 2

BH , THF3

H O , NaOH22

CH – C CH3

(A)Major

(B)Major

NaBH ,HO4

Relationship between (A) and (B) are(A) Diastereomers (B) Positional isomer (C) Functional isomer (D) Identical



CHEMISTRY78. Which of the following curve is correct for an ideal gas of fixed mass at constant temperature ?

(A)

logP

logV

(B)

PV

1V2

(C)

PV

1V2

(D)

PV2

V

79. As two atoms approch each other in space, the potential energy initially decreases and then increases asshown in the diagram below.

Energy(KJ/mole)

1 2 3 4Inter nuclear distance(A )0

Correct two changes attributed to above diagram areFrom 4 to 1.5 A0 From 1.5 to 0 A0

(A) Proton - Electron attraction increases Proton - Proton repulsion increases(B) Proton - Electron attraction increases Electron - Electron repulsion decreases(C) Proton - Electron attraction decreases Electron - Electron repulsion increases(D) Proton - Electron repulsion decreases Proton - Proton repulsion decreases




CHEMISTRY80. An unknown compound C6H12 (K), decolorises Br2 and is oxidised by hot acidified KMnO4 to a resolvable

carboxylic acid, C4H9COOH. Identify K.

(A) CH3

CH3H2C(B)

CH3

CH3H2C (C) CH3

CH3H2C(D)

CH3

CH3H2C

81. Decomposition of H2O2() shows first order kinetics. If rate of decomposition of H2O2 is 3.4 g/min.Then rate of formation of O2 in(g/sec) is :(A) 1.6 (B) 0.0266 (C) 6.8 (D) 0.113

82. Select incorrect statement for a diatomic homonuclear +2 cation having molecular orbital configuration(1s)2 (*1s)2 (2s)2 (*2s)2 (2p)2 (2p)4

(A) Ion is diamagnetic (B) It's neutral diatomic molecule is paramagnetic(C) s-p mixing occurs (D) It has higher bond order than respective neutral molecule

83. cis-2-butene CH CO H3 3

anhydrous (P)

(P) formed is(A) meso (B) trans (C) racemic (D) pair of diastereomers



CHEMISTRY84. For given zero order reaction A B + C. If initial concentration of A is 2M and rate of reaction is 2×10–2M/sec.

then half life of reaction is :(A) 25 sec (B) 50 sec (C) 100 sec (D) 60 min

85. The oxide of certain element 'E' in its group oxidation state has the following structural forms 1, 2, 3

EOO

OOE

OO

OE

OO

O n(1)

(2)

E

O

O O

EE OO

O

(3)

EO O

O

Element 'E' is(A) Silicon (B) Phosphorous (C) Sulphur (D) Chlorine

86. In Lassaigne test, In case Nitrogen and sulphur both are present in an organic compound, What is the colourof complex?(A) Blood Red (B) Blue (C) Violet (D) Black

87. On heating, compound 'X' gives amphoteric coloured oxide, paramagnetic acidic coloured gas and a neutralparamagnetic colourless gas. Compound 'X' is :(A) CrSO4 (B) Pb(NO3)2 (C) ZnCO3 (D) (HCOO)2Be



CHEMISTRY88. In following redox reaction

x Fe+2 + y Cr2O72– + 14H+ x Fe+3 + 2Cr3+ + z H2O

The value of x, y, z are(A) x = 6, y = 1, z = 7 (B) x = 3, y = 6 z = 8(C) x = 6 y = 2, z = 7 (D) x = 4, y = 6, z = 7

89. Ph – CCH Hg+2

dil. H SO2 4 (A)

Major product (A) is

(A) Ph–CH2–CHO (B) Ph–C–CH3

O(C) Ph–CH2–CH2–OH (D) Ph–CH–CH3

OH

90. Given for parallel reaction

A

k1

k2

B

C

k1 = 0.7 × 10–2 min–1 ; k2 = 2.1 × 10–2 min–1 ; ln2 = 0.7Which is correct statement ?(A) Percentage distribution of B in product is 75%.(B) Half life period for disappearance of A is 100 min.(C) Rate constant of disappearance of A is 2.8 × 10–2 min–1.(D) Concentration of B and C are present in equal proportion after 10 min.








B. Question paper format :9. The question paper consists of 3 parts (Physics, Chemistry and Mathematics).

10. Parts contains 30 multiple choice questions. Each question has 4 choices (A), (B),(C) and (D) for its answer, out of which only one is correct.

C. Marking Scheme :

11. For each question in Parts, you will be awarded 4 marks if you have darkened onlythe bubble corresponding to the correct answer and zero mark if no bubbles aredarkened. In all other cases, minus one (–1) mark will be awarded.


CODE - ADATE : 24-04-16

REVIEW TEST–2 (MEGA PHASE-I COURSE-2017)JEE Advance (Paper-1)



















CODE - A


DATE : 15-05-16

Vibrant Academy (I) Pvt. Ltd. "A-14(A)" Road No.1, Indraprastha Industrial Area, Kota (Raj.) Ph. 0744-2423406 [RT-2,P-1,A-2]

PART I : MATHEMATICSSECTION - I

Integer Answer TypeThis section contains 8 questions. The answer to each of the questions is a single-digit integer, ranging from0 to 9. The appropriate bubbles below the respective question numbers in the ORS have to be darkened. Forexample, if the correct answers to question numbers X, Y, Z and W (say) are 6, 0, 9 and 2, respectively, thenthe correct darkening of bubbles will look like the following :In all cases round answer to nearest integer value (if required)

0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

1. If f(x) = 0h

lim

h

)x(sin–))hx(sin( xln)hxln( find f(/2)

2. If f(x) = (2x – 3)25 + 34

x + cosx and g(x) be its inverse. Let g(2) = qp

where p and q are prime numbers find

q – p.



MATHEMATICS


3. Let

9

0r2r2

20r2

20 CC = 1aa (39C21 – 19C10) find the number of divisors of a.

4. Let f(x) be a biquadratic function of x such that 0xlim

x1

3x2)x(f

= e–3 , then find |f(1)|

5. Let there exists real number a and b such that for every positive number x, the identity

tan–1

8x

x1

+ tan–1 (ax) + tan–1 (bx) = 2

holds. Let a2 + b2 = qp

where p and q are relatively prime

positive integers. Find (p + q).


MATHEMATICS


6. The minimum radius of the circle represented by family of circles x2 + y2 + kx + (k + 1)y – (k + 1) = 0 is r.

Find the value of 2r1

.

7. If f is continuous and differentiable function such that f(f(x)) = 1 + x x R. Find f (2016).

8. Let a, b, c be positive real numbers such that 1c1

b1

a9

and S be the minimum value of abc find log3(S).


MATHEMATICS


SECTION - IIMultiple Correct Choice Type

This section contains 10 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for itsanswer, out of which ONE OR MORE is/are correct.

9. In which of the following cases limit exists at the indicated point.

(A) f(x) = x

|]x|x[ at x = 0 where [.] denotes greatest integer function

(B) f(x) = x/1

x/1

e1xe

at x = 0

(C) f(x) = (x – 3)1/5 sgn(x – 3) at x = 3, where sgn denotes signum function

(D) f(x) = x

|x|tan 1 at x = 0

10. Consider f(x) = max (|tanx|, |cosx)| in (–, ) which of the following statement(s) is/are correct.(A) f(x) is discontinuous at 2 points (B) f(x) is non-derivable at exactly 4 points.(C) f(x) is discontinuous at 4 points (D) f(x) is non-derivable at exactly 6 points.

11. Consider two circles, one touching x-axis at A(2, 0) and has radius 1 unit and the other touching x-axis atB(6, 0). Let C and D be the centres of first and second circle respectively let P(6, 2) be a point on a lineperpendicular to CD and bisecting AB. If PA and PB intersect respective circles at E and F, then

(A) PFPE

= 51

(B) 5PFPE

(C) (PE) (PF) = 564

(D) (PE) (PF) = 64 5


MATHEMATICS


12. In a ABC 3 sin C = 2sec A – tan A and one of the side is of 2 units length then

(A) C = 2

(B) B = 6

(C) triangle is right angled isoceles

(D) maximum area of ABC is 2 3 sq. units

13. Let f(x) = nlim n2

2n2

)x1(xxsin)x1(xtan

, then

(A) ¯0xlim f(x) = 1 (B) 0x

lim f(x) = 0

(C) 0xlim f(x) = 1 (D) 0x

lim f(x) = 1

14. Let n is a positive integer and 2n 1(3 3 5) ; ; (0, 1), then

(A) is an odd integer (B) Exponent of 2 in ( + ) is 2n + 1

(C) 1n2)533( is not divisible by 3 (D) is divisible by 5

(where [.] denotes greatest integer function)


MATHEMATICS


15. If a ABC if a2 + b2 + c2 = bc ca 3 then

(A) ABC is equilateral triangle (B) ABC is rightangled triangle(C) Angle B, A, C are in A.P. (D) ABC is scalene triangle

16. The last term in binomial expansion of n

3 122

is

3log 8

31

3. 9

then middle term will be

(A) Negative (B) Irrational (C) Positive (D) Rational

17. Two functions f and g have first and second derivatives at x = 0, and satisfy the relations

2f(0) ; f (0) 2g (0) 4g(0)g(0)

; g(0) = 5f(0) = 6f(0) = 3 then

(A) If h(x) = f(x)g(x) then h(0) =

154

(B) If k(x) = f(x) g(x) sinx then k(0) = 2

(C) x 0

g(x) 1limf (x) 2

(D) None of these

18. If cos8x cos7x dx

1 2cos5x

is expressed as K sin 3x + M sin 2x + C then

(A) K = –1/3 (B) K = 1/3 (C) M = – 1/2 (D) M = 1/2


MATHEMATICS


SECTION - IIIMatrix - Match Type

This section contains 2 questions. Each question contains statements given in two columns, which have tobe matched. The statements in Column I are labelled A, B, C and D, while the statements in Column II arelabelled P, Q, R, S and T. Any given statement in Column I can have correct matching with ONE OR MOREstatement(s) in Column II. The appropriate bubbles corresponding to the answers to these questions haveto be darkened as illustrated in the following example :

If the correct matches are A – Q, S and T; B – Q and R; C – P and Q; and D – S and T; then the correctdarkening of bubbles will look like the following.

P Q R S

P

P

P

Q

Q

Q

R

R

R

S

S

S

A

B

C

D

P Q R ST

T

T

T

T

19. Let (x, y) be such that cos–1(ax) – cos–1(by) = cos–1(2xy) ; then

Column-I Column-II

(A) If a = 1, b = 0 , then (x, y) (P) lies on y2(1 + 4x2) = 1

(B) If a = 0, b = 1, then (x, y) (Q) lies on x2 + y2 = 1

(C) If a = 1, b = 1, then (x, y) (R) lies on x2 (1 + 4y2) = 1

(D) If a = 2, b = 1, then (x, y) (S) lies on (1 – 4x2)(1 – y2) = 0

(T) lies on (1 – x2)(1 – 4y2) = 0


MATHEMATICS


20. Find the value of 'a' in each caseColumn-I Column-II

(A) 3 2 4 3 24x 5x 2x 1 dx x ax x x c (P) 23

(B) 3/2dx 2

a(x 1) x 1 x c3x 1 x

(Q)

12

(C) 1

cos x.cos2x dx asinx sin3x c6

(R) 53

(D) 3 1 acos x. dx sin3x sin x c

12 4 (S)

34

(T) 3


PART II : PHYSICSSECTION - I


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9

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1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

21. A portion of straight glass rod of square cross-section of side 3 cm and refractive intex 1.5 is bent into an arcof circle of outer radius R cm and a parallel beam of light is incident on it as shown in the figure. Find thesmallest R (in cm) which permits all the light to pass around the arc.

R



PHYSICS


22. A small block B is supported by a platform connected at A to rod OA. Point A describes a circle in a verticalplane at constant speed vA = 0.7 m/s, while the platform is constrained to remain in horizontal motion.Determine the minimum value of the coefficient of static friction betwen the block and platform if the block is

not to slide. If this minimum value is x, find 21

3x(Length of rod = 0.2 m, g = 9.8 m/s2)

B

O

A

VA

23. A thermally insulated vessel containing one mole oxygen at 27ºC under the 1 atm pressure is acceleratedfrom rest with an acceleration a0 (in m/s2) and is suddenly stopped at the end of 5th second of its motion,

thereby the temperature of oxygen is increased by 3ºC. The acceleration a0 = 50x

(m/s2), find x.

(Treat oxygen as ideal gas)


PHYSICS


24. A biconvex thin lens of radius of curvature R is made-up of variable refractive index | y |2 1d

. Assume

very small aperture (2d << R). A point object O is placed at a distance R = 7.5 m on the principal axis fromthe lens (as shown). Due to variable refractive index of lens, there are infinite numbers of image on theprincipal axis. These image are spreaded over the length l. Find the value of l (in m).

O

RR

yR

d

dx

P

25. A vessel ABCD of 10 cm width has two small slits S1 and S2 sealed with identical glass plates of equalthickness. The distance between the slits is 0.8 mm. POQ is the line perpendicular to the plane AB andpassing through O, the middle point of S1 and S2. A monochromatic light source is kept at S, 40 cm belowP and 2m from the vessel, to illuminate the slits as shown in the figure below. Calculate the position of thecentral bright fringe(in cm) on the other wall CD with respect to the line OQ.

10cm2mS

40cmO Q

S1

S2

B

P

DA

C


PHYSICS


26. A stone weighing 0.5 kg tied to a rope of length 0.5 meter revolves along a circular path in a vertical plane.The tension of the rope at the lowest point of circle is 45 Newton. The rope breaks at the moment whenvelocity is directed upwards. After breaking of rope, find the maximum vertical height (in m) obtained by stonefrom its initial position.

27. An object is placed 21 cm in front of a concave mirror of radius of curvature 10 cm. A glass slab of thickness3 cm and refractive index 1.5 is then placed close to the mirror in the space between the object and the

mirror. If the distance of the final image formed is 20 x

3

cm from the mirror, find the value of x. You may

take the distance of the near surface of the slab from the mirror to be 1 cm

28. A rod of length 6 m has specific gravity (= 25/36). One end of the rod is tied to a 5 m long rope, which in turn

is tied to the floor of a pool 10 m deep, as shown. If length of the part of rod which is out of water is 6 meterx

,

find x.

10 m5 m


PHYSICS




29. A transparent slab of thickness t and refractive index is inserted in front of upper slit of YDSE apparatus.The wavelength of light used is . Assume that there is no absorption of light by the slab. Select the correctstatement(s) :(A) The intensity of dark fringes will be 0, if slits are identical(B) The change in optical path due to insertion of plate is t(C) The change in optical path due to insertion of plate is ( – 1)t

(D) For making intensity zero at the centre of screen, then thickness could be 5

2( 1)

30. Four forces act on a point object. The object will be in equilibrium if(A) All of them are in the same plane.(B) They are opposite to each other in pair.(C) The sum of x, y and z components of force is zero separately.(D) They form a closed figure of 4 sides when arranged in order.

31. A single conservative force acts on a 1 kg particle that moves along x-axis. The potential energy of theparticle varies with x as U = 20 + (x –2)2, here U is in joules and x is in joules and x is in meters. When theparticle is at x = 5 m, its kinetic energy is 20 J. Then which of the following is/are correct ?(A) Mechanical energy of particle is 49 J.

(B) Least and greatest value of x between which particle can move is 2 – 29 m and 2 29 m respec-

tively.(C) Maximum kinetic energy of the particle is 29 J.(D) At x = 2, the body is in equilibrium.



PHYSICS32. A gas expands such that its initial and final temperature are equal. Also, the process followed by the gas

traces a straight line on the p–V diagram(A) The temperature of the gas remains constant throughout(B) The temperature of the gas first increases and then decreases(C) The temperature of the gas first decreases and then increases(D) The straight line has a negative slope

33. A liquid flows through a horizontal tube. The velocities of the liquid in the two sections, which have areas ofcross section A1 and A2 are v1 and v2 respectively. The difference in the levels of the liquid in the two verticaltubes is h. Then

A2

h

A1 v1 v2

(A) The volume of the liquid flowing through the tube in unit time is A1v1

(B) 2 1v v 2gh

(C) 2 22 1v v 2gh

(D) The total energy per unit mass of the liquid is the same in both sections of the tube

34. In Young’s double slit experiment two wavelength of light are used simultaneously where 2 = 21. In thefringe pattern observed on the screen.(A) Maxima of wavelength 2 may coincide with minima of wavelength 1

(B) Fringe width of 2 will be double that of fringe width of 1 and the nth order maxima of 2 will coincide with2n order maxima of 1.

(C) nth order minima of 2 will coincide with 2nth order minima of 1

(D) None of the above



PHYSICS35. Which of the following graphs is/are valid for the motion of a solid sphere projected with a velocity v0 in a

gravity free viscous liquid? (x, v, a, t are displacement, velocity, acceleration, time respectively)

v0

(A) t

x

O

(B) t

x

O

(C) v

a

O

(D) x

v

O

36. Water rises in a vertical capillary tube of glass. Angle of contact is zero. Choose the correct option(s)(A) If the capillary tube is tilted from vertical, length of water column will change in capillary(B) Heat produced in the process of rise is equal to increment in gravitational PE of water that rises(C) Heat produced in the process of rise is half of increment in gravitational PE of water that rises(D) Height of water column will change if capillary’s open end is gently capped air tight



PHYSICS37. Water flows through a narrow tube, whose area of cross-section at A is twice that at B. A is area of cross-

section of piston of mass M and atmospheric pressure 0MgPA

. Choose the correct option(s). ( is density

of liquid)

A B

h

M

(A) Speed of eflux at B with piston is 02(P gh)

(B) Speed of eflux at B without piston is 2gh

(C) Without piston, pressure at A is (P0 + 34

gh)

(D) Without piston, pressure at A is 2Mg 3 gh

A

38. Take the z-axis as vertical and xy plane as horizontal. A particle A is projected with speed of 4 2 m/s at an

angle 45º to the horizontal in the xz. Particle B is also projected at same instant but with speed 5m/s at anangle tan–1(4/3) with horizontal in yz plane, then which of the following statement/s is/are correct ?(g=10m/s2)(A) Magnitude of relative velocity of A with respect to B is 5m/s during motion(B) Particle A and B again hit the ground at the same instant(C) The separation between A and B when they hit the ground is 4m(D) The path of A with respect to B is straight line when they are in air



PHYSICSSECTION - III

Matrix - Match TypeThis section contains 2 questions. Each question contains statements given in two columns, which have tobe matched. The statements in Column I are labelled A, B, C and D, while the statements in Column II arelabelled P, Q, R, S and T. Any given statement in Column I can have correct matching with ONE OR MOREstatement(s) in Column II. The appropriate bubbles corresponding to the answers to these questions haveto be darkened as illustrated in the following example :


P Q R S

P

P

P

Q

Q

Q

R

R

R

S

S

S

A

B

C

D

P Q R ST

T

T

T

T

39. Column I Column II(A)Block of mass 2 kg on a rough horizontal surface (P) Tension at the mid point of block is 10 N

pulled by a horizontal force of 20 N, coefficient offriction = 0.5

(B)Block of mass 2 kg pulled with constant speed up an (Q) Acceleration of block is 5m/s2

incline of inclination 30° and coefficient of friction 1/ 3

(C)Block of mass 0.75 kg pulled by a constant force of (R) Force of friction acting is 15 N7.5 N up on incline of inclination 30° and coefficient of

friction 1/ 3

(D)Block of mass 2 kg pulled vertically by a force 20 N (S) Resultant force on the block is zero(T) Force of friction is 10 N


40. Column-I Column-II

Optical system of glass 32

placed in air

(A) (P) Image may be vitrual when object is real

Equi-convex lens polished on one surface

(B)

R1 R2

(Q) Image may be real when object is virtual

Convexo-concave lens, surface of largercurvature radius polished

(C)Concave lens with different curvature radii (R) Image may form on real object itself

(D)Plano convex lens mirror on plane surface (S) Image may be real with object real

(T) Image may be at

PHYSICS



PART III : CHEMISTRYSECTION - I


0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

41. Number of alkenes (structural isomer) of ‘C6H12’ which give 3-bromo-3-methyl pentane when ever react withHBr.

42. A radioactive element X (atomic weight = 200) show activity 6.93 × 1015 dps. If weight of X is represented as(m × 10–n) g. What is the value of (m + n) ?[Given : t1/2 = 100 min ; NA = 6 × 1023]



CHEMISTRY


43. Pyrosulphurous acid + Excess NaOH solution )saltSodium(

'P' + 2H2O

Find the value of expression |x – y| for salt ‘P’.Where x = total number of adjacent bond angles y = maximum number of equal bonds length.

44. “X” geometrically isomeric dicarboxylic acids ; ‘C4H4O4’ Bayer reagent “Y” products

So identify (X + Y) is :

45. The number of reaction(s) among following which holds true for given graph.

C

PKKlog

log(RT)45º

(i) 2NH3(g) N2(g) + 3H2(g) (ii) NH4HS(s) NH3(g) + H2S(g)

(iii) CaCO3(s) CaO(s) + CO2(g) (iv) CuSO4.5H2O(s) CuSO4.3H2O(s)+2H2O(g)

(v) PCl5(g) PCl3(g) + Cl2(g) (vi) N2O4(g) 2NO2(g)

(vii) 2SO3(g) 2SO2(g) + O2(g)


CHEMISTRY


46. In which of the following molecular species bond order between central atom and oxygen is not equal to twoClO3, NO2, XeO3, ClO2, N2O5, NO+, XeO6

4–, POR3, C3O2

47. How many alkynes (excluding stereoisomers) having molecular formula C6H10 will give H2 gas by NaH.

48. A green plant contains radioactive 14C and stable 12C isotope. If in a sample of dead old wood of this plant2.5 × 10–6 mol 14C and 7.5 × 10–6 mol 14N are present then calculate value of Z,

where 141/2

Age of wood(t)ZHalf life of C isotope(t )

:


CHEMISTRY




49. Given ;

B(g)

2C(g)

3D(g)

A(g)k 1

k2

k3

k1 = 0.35 × 10–3 sec–1

k2 = 0.70 × 10–3 sec–1

k3 = 1.05 × 10–3 sec–1 (ln2 = 0.7)If initially pure A was taken in a closed rigid container with 10 atm pressure. Which is/are correct statement(s)?(A) Pressure of A(g) is 1.25 atm after 1000 sec.(B) Rate constant of disappearance of A is 2.1 × 10–3 sec–1

(C) Rate constant of disappearance of A is 4.9 × 10–3 sec–1

(D) Rate constant of appearance of C is 1.4 × 10–3 sec–1

50. For which of the following compound(s) the value of x 2(A) Hx[Co(CO)4] (B) [Mn(CO)(NO)x] (C) [Fe(CO)4]x– (D) [Cr(-C6H6)x]

51. Which of the following can’t follow SN2 mechanism ?(A) Allyl chloride ; CH2 = CH – CH2 – Cl (B) Vinyl chloride ; CH2 = CH – Cl

(C) Chloro benzene ;

Cl

(D) Benzyl chloride ;

CH Cl2


CHEMISTRY


52. Which is/are correct graph for given reactions?

(A) First order kinetics (A B)ln A

t

(B) zero order kinetics (A B)A

t

(C) Radioactive decay (A B) T0.5

Temp.

(D) 2nd order kinetics (A B) T0.5

A0

53. In Bohr's model of hydrogen-like species, which of the following is true ?(A) KE of electron in ground state of hydrogen atom is equal to KE of electron in n = 3 state of Li2+ ion.(B) KE of electron in n = 3 state of hydrogen is equal to KE of electron is ground state of Li2+ ion.(C) Energy of hydrogen atom in its ground state is equal to energy of Li2+ ion in n = 2 state(D) Potential energy of electron in ground state of hydrogen atom is equal to potential energy of electron infirst excited state of He+ ion.


CHEMISTRY


54. Select INCORRECT IUPAC name of coordination compounds is/are(A) [CoBr(NH3)5]Br2 : Pentaamminebromidocobalt(III) dibromide(B) [Ir(SCN)(H2O)(en)2]2+ : Aquabis(ethylenediamine) thiocyanato-S-irridium(III) ion(C) [Cu(trien)][PtCl4] : Triethylenetetraaminecopper(II) tetrachloridoplatinum(II)(D) Fe4[Fe(CN)6]3: Iron hexacyanidoferrate(II)

55. Which alkyne reacts with HgSO4/dil.H2SO4 to give ketone.

(A) HC CH (B) CH3 – C CH (C) CH3 – C CH3 (D) Ph – C CH

56. Correct statement above this compound.

CC CHH

Br Br

(A) Plane of symmetry present (B) Centre of symmetry present

(C) C2 ; axis of symmetry present (D) Chiral compound



CHEMISTRY57. 0.1 mol of K2Cr2O7 is completely react with HCl and form CrCl3 and Cl2 gas according to given reaction

K2Cr2O7 + HCl CrCl3 + Cl2 + KCl + H2OIf all the Cl2 is allowed to react with KI solution in presence of acetic acid so that I2 produced is estimated by1 M hypo solution.Which of the following is/are correct?(A) Equivalent weight of HCl is 85.16(B) 0.6 mol of electrons is transfer during redox(C) 0.6 mol of HCl is used as reducing agent(D) 600 ml of hypo solution is required for estimation of Iodine

58. CORRECT statement(s) for F2 is/are.(A) Both HOMO and LUMO have centre of symmetry(B) Energy gap between HOMO and LUMO : F2 > I2(C) Bond length : B2 > F2

(D) Ionization energy : F2 > O2



CHEMISTRYSECTION - III



P Q R S

P

P

P

Q

Q

Q

R

R

R

S

S

S

A

B

C

D

P Q R ST

T

T

T

T

59. Column-I Column-II(Salt) (Characteristics)

(A) FeSO4(s) (P) Thermal decomposition occurs through redox reaction

(B) Sn(NO3)2(s) (Q) Coloured residue is obtained

(C) CrSO4 (s) (R) Two different acidic gases are evolved

(D) Cu(OH)2.CuCO3 (s) T 800ºC (S) Obtained residue reacts with dilHCl

(T) Thermally less stable than BaSO4


60. Column-I Column-IIPair of compounds Relationship

(A) & (P) Enantiomer

(B)Cl

F

Cl Br

CH3

CH3

&Cl

Br

Cl F

CH3

CH3

(Q) Identical

(C)

HH

H

HNH2

NH2

&H

NH2

H

HNH2

H(R) Positive lassigne test

(D)

Br

&

Br

(S) Diastereomers

(T) Conformers


CHEMISTRY








B. Question paper format :9. The question paper consists of 3 parts (Mathematics, Physics and Chemistry).

Each part has 3 sections.

10. Section I contains 8 questions. The answer to each of the questions is aninteger, ranging from 0 to 9. The answer will have to be appropriately bubbled in theORS as per the instructions given at the beginning of the section.

11. Section II contains 10 multiple choice questions. Each question has 4 choices(A), (B), (C) and (D) for its answer, out of which one or more is/are correct.

12. Section III contains 2 questions. Each questions has four statements (A, B, C and D)given in Column I and five statements (P, Q, R, S and T) in Column II. Any givenstatement in Column I can have correct matching with one or more statement(s)given in Column II. For example, if for a given question, statement B matches with thestatements given in Q and R, then for that particular question, against statement B,darken the bubbles corresponding to Q and R in the ORS.

C. Marking Scheme :

13. For each question in Section-I, you will be awarded 4 marks if you darken thebubble corresponding to the correct answer and zero mark if no bubbles is darkened.No negative marks will be awarded for in this Section.

14. For each question in Section-II, you will be awarded 4 marks if you have darkenedonly the bubble corresponding to the correct answer and zero mark if no bubbles aredarkened. In all other cases, minus two (–2) mark will be awarded.

15. For each question in Section III, you will be awarded 2 marks for each row inwhich you have darkened the bubble(s) corresponding to the correct answer and zeromark if no bubbles are darkened. In all other cases, minus one (–1) mark will beawarded. Thus, each question in this section carries a maximum of 8 marks.


CODE - ADATE : 15-05-16




















CODE - A


DATE : 15-05-16

Vibrant Academy (I) Pvt. Ltd. "A-14(A)" Road No.1, Indraprastha Industrial Area, Kota (Raj.) Ph. 0744-2423406 [RT-2, P-2,A-2]



0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

1. If y = cosx ; then find the value of 2

72

dy)x(sind

at x = 2

.

2. If

2015

0n2015n 77

1 = k20107

144

where k is a natural numbers. Find k.



MATHEMATICS


3. If f(x) = max. {x, x2} and g(x) = f(f(x)). If dxd

(g–1(x)) at x = 16 is denoted by then find the value of 81

.

4. If 3 f(x) + 2f x 54 10x 30x 1

, then find the sum of the digits of f(0) :

5. If the system of equations x + 2y + 3z = 4, x + py + 2z = 3 and x + 4y + µz = 3 has an infinite no of solutionsthen f + µ =


MATHEMATICS


6. Let f(x) x2 – 3x + 3 and x1, x2, x3 and x4 be solution of the equation f(f(x)) = x. Then the number ofarrangements of x1, x2, x3 and x4, taken all at a time, is

7. Find the largest value of n for which the inequality (n + 1)C6 + nC4 < (n + 2)C5 – nC5 holds.

8. Let f : [1, ) R be the function defined by f(x) = x

}x{]x[

where [.] and {.} denote greatest integer function and fractional part function respectively let z be the smallestreal number such that f(x) z, for all x 1. Find z2


MATHEMATICS


SECTION - IISingle Correct Choice Type


9. If 194)34–7()347( ]x[]x[ , then x lies in thernal

(A) [2, 3) (B) [–3, –2) (C) [1, 2) (D) [–2, –1)

10. If x 2x 9x[sinx]

2 5 10

, then the number of solutions in the interval (30, 40) is

(A) 0 (B) 1 (C) 2 (D) infinite

11. Let A and B have coordinates (x1, y1) and (x2, y2) respectively. We define the distance between A and B asd (A, B) = max { | x2 – x1 | , | y2 – y1 | }

If d (A, O) = 1, where O is the origin, then the locus of A has an area of(A) 1 sq. unit (B) 2, sq. units (C) 4 sq. units (D) 1/4 sq. units

12. The value of determinant

4sinB1 cos Ab

2a 8sin A 13a 12sin A cosB

is where (a, b and c are the sides of a triangle and A, B

and C are angles opposite to a, b and c respectively)(A) 0 (B) 1 (C) 2 (D) 3


MATHEMATICS


13. There exists positive integers A, B and C with no common factors greater than 1, such thatA log200 5 + B log200 2 = C. The sum A + B + C equals

(A) 5 (B) 6 (C) 7 (D) 8

14. If 2

x 1 5x 7

(x) x 1 x 1 82x 3x 0

= ax3 + bx2 + cx + d, then find c + d =

(A) 0 (B) 17 (C) 21 (D) 1

15. 0xlim

21–

x1x2sin

x1

= ? (where [.] is G.I.F.).)

(A) 21

(B) 1 (C) 2 (D) – 2

16. 1xlim

tan( x)212 –

x

(A) e2 (B) e2/ (C) e–2/ (D) e–/2


MATHEMATICS


SECTION - IIIComprehension Type

This section contains 2 groups of questions. Each group has 2 multiple choice questions based on aparagraph. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONE OR MOREis/are correct.

Paragraph for Question Nos. 17 to 18Real the following write up carefully and answer the following questions :Consider a quadratic function f(x) = ax2 + bx + c (a, b, c R, a 0) and satisfying the following conditions(i) f(x – 4) = f(2 – x) x R and f(x) x x R

(ii) f(x) 2x 1 x (0,2)

2

(iii) The minimum value of f(x) is zero17. The value of the leading coefficient to the quadratic polynomial is

(A) 14

(B) 13 (C)

12

(D) 1

18. f(1) has the value equal to

(A) 14

(B) 13 (C)

12

(D) 1



MATHEMATICSParagraph for Question Nos. 19 to 20

Let F : R R be a differential function satisfying x y 2 f(x) f(y)f

3 3

for all x and y and f' (2) = 2, then

19. The value of f(1) is(A) 0 (B) 2 (C) 4 (D) 6

20. if g(x) = |f(|x|)–3| for all x R, then g(x)(A) one Non-differentiable point(B) two Non- differentiable point(C) There non-differentiable point(D) four non-differentiable point




0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

21. As shown in the figure, there is no friction between the horizontal surface and the lower block (M = 3kg) butfriction coefficient between both the blocks is 0.2. Both the blocks move together with initial speed v towardsthe spring, compresses it and due to the force exerted by the spring, moves in the reverse direction of theinitial motion. What can be the maximum value of v so that during the motion, there is no slipping between

the blocks. (use g = 10m/s2) If this max value of v is 1x

meter/sec, find x.

M

1kg µ=0.2

3kg

K = 400N/m m

= 0

22. A trolley C shown in the figure is begun to be driven with constant acceleration a = 3 m/s2 under some force.Assume pulleys are massless and friction is absent everywhere. Find the speed (in m/s) of block B, 4second after beginning of motion. Thread is long enough. (Mass of A = 10 kg, mass of B = 5 kg)

C a

A

B



PHYSICS


23. A plano-convex lens has a thickness of 4 cm. When placed on a horizontal table, with the curved surface incontact with it, the apparent depth of the bottom most point of the lens is found to be 3 cm. If the lens isinverted such that the plane face is in contact with the table, the apparent depth of the centre of the plane

face is found to be 25 cm8 . The radius of curvature of the convex surface of the lens is 1 m

x

. Find the value

of x?

24. A string of length 25 cm and mass 2.5 g is under tension is clamped at both ends. When the string is setvibrating in its first ovetone and a tuning fork (frequency 200 Hz) is vibrated, 8 beats per second are heard. Itis observed that decreasing the tension in the string decreases the beat frequency. Find the tension(in Newton) in the string. If this tension is (3x) Newton, find x

25. A solid block (mass = 1 kg), is moving with a constant speed (v0 = 9 cm/s) on a plank P of mass 3kg2

under

some external force. The friction coefficient between the upper surface of P and the block is = 0.3, while thelower surface of P is smooth and rests on the ground. Initially, P is fixed to the ground by a pin T. If T issuddenly removed, find the acceleration (in m/s2) of P.

TP

v = 9 m/s0


PHYSICS


26. A steel wire of length 1 meter, mass 0.1 kg and uniform cross-section area 10–6 m2 is rigidly fixed at bothends. The temperature of wire is lowered by 20°C. If transverse waves are set up by plucking the string in themiddle and the frequency with which wire vibrates is (10 + x) Hz, find the value of x. (Coefficient of linearexpansion = 1.21 × 10–5(°C)–1, Young’s modulus y = 2 × 1011 N/m2)

27. A motoboat going downstream overcome a bottle floating in river at a point A. After 30 minutes, it turned backand after some time passed the bottle at a distance 7.0 km from the point A. Find the flow velocity (in km/h)assuming the duty of the engine to be constant.

28. n drops of water, each of radius 2 mm, fall through air at a terminal velocity of 8 cm/s. If the coalesce to forma single drop, then the terminal velocity of the combined drop is 32 cm/s. Find the value of n :


PHYSICS




29. Two identical straight wires (1) and (2) are stretched so as to produce 6 beats per second when vibratingsimultaneously. Tension in (1) is more than tension in (2). Wires always vibrate in fundamental mode.If length of both wires is halved and tension remains same the beat frequency is change to.(A) 3 (B) 2 (C) 7 (D) None of these

30. Choose the correct option.(A) Whenever heat is supplied to a gas, its internal energy increases.(B) Internal energy of gas must increase when its temperature is increased.(C) Internal energy of gas must increase when work is done on the gas.(D) Internal energy of gas is proportional to square of the average velocity of the vessel in which gas iscontained.

31. An upright U-tube manometer with its limps 0.6m high and spaced 0.3m apart contains a liquid to a height of0.4m in each limb. If the U-tube is rotated at 10 radian/second about a vertical axis at 0.1m from one limb.z1 & z2 are heights of liquid columns on rotation. Choose the correct option.

0.1m 0.2m

z2

z1

0.4m

10rad/s

(A) z1 = 0.35 m (B) z2 = 0.5 m (C) z1= 0.3 m (D) None of these


PHYSICS


32. Capillary action is NOT attributed to :(A) Cohesion (B) Adhesion (C) Surface tension (D) Viscocity

33. A thin slice is cut of a glass cylinder along a plane parallel to its axis. The slice is placed on a flat glass plateas shown in figure. The observed interference fringes from this combination shall be

(A) Straight (B) Circular(C) Equally spaced (D) Having fringe spacing which increases as we go outwards

34. Two point monochromatic and coherent sources of light of wavelength are placed on the dotted line in frontof an infinite screen. The source emit waves in phase with each other. The distance between S1 and S2 is dwhile their distance form the screen is much larger. Choose the incorrect option.

d

S1 S2 O

(A) If d is 32

, at O minima will be observed

(B) If d is 116

, then intensity at O will be 34

of maximum intensity

(C) If d is 3, O will be a maxima

(D) If d is 76

, the intensity at O will be equal to maximum intensity..


PHYSICS


35. White light is used to illuminate the two slits in a Young’s double slit experiment. The separation between theslits is b and the screen is at a distance (d >> b) from the slits. At a point on the screen directly in front of oneof the slits, certain wavelengths are missing. Some of these missing wavelengths are

(A) 22b

3d (B)

22bd

(C) 2b

3d (D) None of these

36. A liquid of density is filled in a vessel of cross-sectional area A upto height h. A block of mass M and cross-sectional area a is made to float in it as shown in figure. The pressure at the bottom of the vessel will be

M

a P0

h

A

(A) P0 + hg (B) P0 + hg + aMg

(C) P0 + hg + A

Mg(D) None of these


PHYSICS




Paragraph for Question Nos. 37 to 38When we look at the sky in a clear night, we find the sky full of stars, filling every portion of the sky almostuniformly. But on a very careful observation through highly sophisticated instruments, one would observedark areas in portions of the observable universe devoid of stars. Such a region is known as a dark nebula. Adark nebula is basically a cold gas cloud in interseller space that contains enough material to block out lightfrom stars behind it. A typical dark nebula is about 20 light years in diameter and contains about 50 hydrogenatoms per cubic centimeter (monatomic hydrogen, not H2) at a temperature of about 20K. (A light year is thedistance light travels in vacuum in one year and is equal to 9.46 × 1015m.)

37. What would be the RMS speed of monatomic hydrogen?(A) 653 m/s (B) 689 m/s (C) 703 m/s (D) 741 m/s

38. What would be the pressure inside a dark nebula?(A) 1.4 × 10–12Pa (B) 2.8 ×10–14 Pa (C) 2.8 × 10–12 Pa (D) 1.4 × 10–14 Pa


Paragraph for Question Nos. 39 to 40A concave mirror of radius of curvature 20 cm is shown in the figure. A circular disc of diameter d variable withtime t as d = (1.0 + 0.2t) cm (where t is time in sec.) is placed on the principal axis of mirror with its planeperpnedicular to the principal axis at a distance 15 cm from the pole of the mirror.

||||||||||||| |||| |||||||||||||||||||||||

20cm

’;

39. The image formed by the mirror will be in the shape of a(A) Circular disc (B) Elliptical disc with major axis horizontal(C) Elliptical disc with major axis vertical (D) Distorted disc

40. What will be the rate at which the horizontal radius of image changes at t = 1 sec.(A) 0.2 m/s increasing (B) 0.2 cm/s decreasing(C) 0.4 cm/s increasing (D) None of these

PHYSICS





0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

41. At 400 K temperature the half life period of first order decomposition of H2O2 is 6 hours. The activation energyof reaction is 11.64 kJ mol–1. Calculate the time (in hours) required for 87.5% decomposition at 500 K temp.[Given in 2 = 0.7]

42. Find total number of species having bond length less than C2 among given speciesB2, N2

+ , C22– , O2

+ , O2– , O2

2– , F2, N2, O2.



CHEMISTRY


43. No. of plane of symmetry in the twistane is

44. From following list of ligands, find the value of expression [x + y – z]

gly, NO2–, bcac, S2O3

2–, , NO3–, SCN– , acac, dipy

where, X = total number of bidentate ligand(s) that form five membered ring with central metal atom/ion.Y = Total number of ambidentate ligand(s) with flexidentate character.Z = Total number of -acid ligands that can form -complex.

45. Calculate the value of Z. where Z = 2x – y. (Given : 20823290 82Th Pb x y )


CHEMISTRY


46.

CH3

CH CH2 3

BrHCl /light2

Number of isomeric products possible after monochlorination is

47. Maximum number of atom(s) lying in a plane in stable configuration of S2F10 molecule.

48. No. of isomer of C4H8 which give racemic mixture whenever react with Br2, CCl4.


CHEMISTRY




49. What is pH of Mg(OH)2 solution at 25°C ? [Given : Ksp[Mg(OH)2] = 5 × 10–16](A) 5 (B) 8.5 (C) 9 (D) 9.5

50. Which compound do not give unsaturation test (Br2/CCl4 or dilute KMnO4).

(I) (II)

(III) CH3 – C C – CH3 (IV)

(A) I, II (B) II, IV (C) I, II (D) I, IV

51. Which of the following option is incorrect?(A) In -decay mass number decreases by four units and the atomic number decreases by two units.(B) Forces that bind the nucleons together are of short range order.(C) Neutron rich nuclei achieve stability by emitting –-particles.(D) Generally nuclei that have odd number of both neutron and proton are more stable than that of even-even

type.


CHEMISTRY


52. On adding KI into aqueous solution of complex ion [Ag(NH3)2]+, yellow coloured precipitate of AgI is obtained,similarly when HI acid was added into complex ion [Ag(NH3)2]+, again precipitate of AgI is obtained. Then theINCORRECT statement(s) for the above observations is/are(A) Complex ion [Ag(NH3)2]+ is imperfect with respect to KI(B) Complex ion [Ag(NH3)2]+ is perfect with respect to KI(C) HI acid neutralizes NH3 ligands and precipitates AgI(D) IUPAC naming of complex is Diamminesilver (I) ion

53. Rate of SN2

I II

( )I ( )II ( )III

(A) I > II > III (B) III > I > II (C) II > III > I (D) III > II > I

54. The molecule that has no tendency for dimerization in gaseous phase :(A) BeCl2 (B) BH3 (C) BeF2 (D) AlCl3


CHEMISTRY


55. Select correct statement with reference to Vander Waal gas(A) The compressibility factor for gas at critical state is 8/3.(B) At critical temperature real gas behaves like an ideal gas(C) At Boyle's temperature real gas behaves like an ideal gas at high pressure(D) At Boyle’s temperature gas can not be liquified.

56. The major product of the following reaction is

NO2

F

BrMe

PhS Na

- +

dimethylformamide

(A)

NO2

F

Me SPh

(B)

NO2

F

Me SPh

(C)

NO2

SPh

Me Br

(D)

NO2

SPh

Me SPh


CHEMISTRY




Paragraph for Question Nos. 57 to 58Some ligands contain low energy level vaccant *-M.O. or d-orbitals, such ligands can effectively participatein back bonding when they form complex compound with transition metal atom/ion. These ligands are called-acid / -acceptor ligands.

57. Which of the following ligand does not act as -acid / -acceptor ligand

(A) H C—CH2 2

CH

(B) 2CH – CH CH

(C) O2 (D) N2

58. For which of the following nonclassical complex compound, Cr–C bond order has higher value(A) [Cr(CO)3(–C6H6)] (B) [Cr(PF3)3(CO)3](C) [Cr(CO)3(–C5H5)]– (D) [Cr(dien)(CO)3]


CHEMISTRY


Paragraph for Question Nos. 59 to 60Decomposition of compound A takes place according to first order kinetics as following.

A B + C

The observed rotation of mixture after 100 min was 10º while after completion of reaction it was –40º.Optical rotation per mol of A, B and C are 30º, 20º and –40º.(Given : ln 2 = 0.7, ln 2.5 = 0.92).

59. Half life period of decomposition of A is :(A) 50 min (B) 100 min (C) 150 min (D) 200 min

60. Reading of polarimeter is zero after :(A) 131.43 min (B) 200 min (C) 262.86 min (D) 65.71 min









CODE - A



10. Section I contains 8 questions. The answer to each of the questions is aninteger, ranging from 0 to 9. The answer will have to be appropriately bubbled in theORS as per the instructions given at the beginning of the section.

11. Section II contains 8 multiple choice questions. Each question has 4 choices (A),(B), (C) and (D) for its answer, out of which only one is correct.

12. Section III contains 2 groups of questions. Each groups has 2 questions based on aparagraph. Each question has 4 choices (A), (B), (C) and (D) for its answer, out ofwhich one or more is/are correct.

C. Marking Scheme :

13. For each question in Section-I, you will be awarded 4 marks if you darken thebubble corresponding to the correct answer and zero mark if no bubbles is darkened.No negative marks will be awarded for in this Section.

14. For each question in Section-II, you will be awarded 4 marks if you have darkenedonly the bubble corresponding to the correct answer and zero mark if no bubbles aredarkened. In all other cases, minus two (–2) mark will be awarded.

15. For each question in Section-III, you will be awarded 4 marks if you have darkenedonly the bubble corresponding to the correct answer and zero mark if no bubbles aredarkened. In all other cases, minus two (–2) mark will be awarded.

DATE : 15-05-16




















CODE - A


DATE : 05-06-16




1. Let f be a real valued function such that for any real x, f(k+x) = f(k–x) and f(2k+x) = –f(2k–x) for somek > 0 then(A) f is even and periodic (B) f is odd but not periodic(C) f is odd and periodic (D) f is even but not periodic

2. The inverse of the function y = x x

x x

10 1010 10

is

(A) log10(2–x) (B) 101 1 xlog2 1 x

(C) 101 log 2x 12

(D) 1 2xlog4 2 x

3. the quadratic equations x2 – 6x + a = 0 and x2 – cx + 6 = 0 have one root in common. The other roots of thefirst and second equations are integer in the ration 4 : 3. The common root is(A) 1 (B) 4 (C) 2 (D) 3

4. Let a, b, c be any real numbers. Suppose that there are real numbers x,y,z not all zero such thatx = cy + bz, y = az + cx and z = bx + ay. Then a2 + b2 + c2 + 2abc is equal to(A) 2 (B) –1 (C) 0 (D) 1




MATHEMATICS

5. Let f(x) = 2 3 2 3

3

sin[e ]x sin[ e ]xsinx

; x 0. ([•] represents G.I.F.) The value of x 0lim f(x) is

(A) 1 (B) –1 (C) 15 (D) – 15

6.x a

4a 3x x 6alim2a 5x 3a 4x

is

(A) 1 (B) 2 (C) 3 (D) 4

7. The number of points of which the function f(x) = 2

1log | x 4 | is discontinuous is

(A) 2 (B) 4 (C) 6 (D) 8

8. The value of sin x2 dxsin x

4

is

(A) x +ln cos x c4

(B) x–ln sin x c

4

(C) x + ln sin x c4

(D) x – ln cos x c

4



MATHEMATICS

9. If f' (3) = 2 then 2 2

2h 0

f(3 h ) f(3 h )lim2h

is

(A) 1 (B) 2 (C) 3 (D) 4

10. If f(x) = tan x sec x 1tan x sec x 1

then f'(x) is equal to

(A) sec x (tan x – sec x) (B) sec x (sec x – tan x)(C) sec x (tan x + sec x) (D) None of these

11. If y = f 3x 45x 6

and f'(x) = tan x2 then dydx is equal to

(A)

2

2

3x 4 12tan .5x 6 5x 6

(B) 2

2

3 tanx 4f5 tanx 6

. tan x2

(C) tan x2 (D) None of these

12. Number of solutions of the equation

sin–1 (tan (tan–1 x + tan–1 (1–x))) = 2

is /are

(A) 0 (B) 1 (C) 2 (D) 3



MATHEMATICS13. The value of the expression

cos (3cos–1x) + sin (3sin–1 x) + tan (3tan–1 x) is

(A) 0 (B) 4x3 – 3x (C) 3x – 4x3 (D) 3

2

3x x1 3x

14. The first two terms of a geometric progression add up to 12. The sum of the third and the fourth terms is 48.If the terms of the geometric progression are alternately positive and negative, then the first term is(A) – 4 (B) – 12 (C) 12 (D) 4

15. If I = 2

7

sec x 7 dxsin x

; the I equals.

(A) 7

tanx c(sin x)

(B) 7

cosx c(sin x)

(C) 7

sin x c(cos x)

(D) None of these

16. In which of the following intervals can x lie, so that it satisfies the inequality 2

2x 1x 12x 5x 2

?

(A) (–2 , 5/2 ) (B) 2 1,3 2

(C) 1 1,3 2

(D) (–2, –1) 2 1,3 2



MATHEMATICS17. For what values of the parameter 'p' does the equation 4x – p (2x) – p + 3 = 0 is satisfied by atleast one real x ?

(A) [–1, ) (B) [0, ) (C) [1, ) (D) [2, )

18. Let a, b, c be the pth, qth, rth terms of a G.P respectively.

Then the value of

p 2

q 2

r 2

loga p plogb q qlogc r r

is :

(A) 0 (B) 1 (C) 2 (D) 3

19. The value of the expression 4 5 6cos .cos .cos .cos

15 15 15 15

is

(A) 5 132

(B) 5 116

(C) 5 18

(D) 5 132



MATHEMATICS20. Let A be the area of square formed by lines 3x2 + 8xy – 3y2 = 0 and 3x2 + 8xy – 3y2 + 2x – 4y –1 = 0. Then

the value of 100A is(A) 5 (B) 10 (C) 20 (D) 30

21. If x, y, z be the length of perpendiculars dropped from circumcentre to the sides BC, CA and AB respectively,of ABC, then a2 + b2 + c2 + 4 (x2 + y2 + z2) = ....... (symbols have usual meaning inABC, ABC is notequilateral)

(A) 3 (a2 + 4x2) (B) 12 (a2 + x2) (C) 12 (a2 + 4x2) (D) 2

2a x4

22. If log4 |x2 + y2| = 1, then the minimum value of |x|– |y| is

(A) 2 (B) –2 (C) 0 (D) can't be determined

23. Let f(x) = min {|x–2|, 2– |x–1|}, then(A) f is discontinous at x = 1 and 2 (B) f is non-differentiable at x = 10(C) f is continous and differentiable at x = 0 (D) f is continous but not differentiable at x = 0


MATHEMATICS


24. If 5 tanx dx

tan x 2 = x + a ln |sin x–2 cos x| + k (where k be an arbitrary constant) then a is equal to

(A) –1 (B) 1 (C) 2 (D) –2

25. The number of integral solutions of the equation a+b+c+d = 25, if a 1, b 3, c 5, d 7 is(A) 8C3 (B) 12C3 (C) 16C3 (D) 4C3

26. Let S = 9999

4 4n 1

1n n 1 n n 1

is , then S equals:

(A) 9 (B) 99 (C) 999 (D) 9999

27. The co-efficient of t50 in (1 + t2)25 (1+ t25) (1+ t40) (1+ t45) (1+ t49) is(A) 1+ 25C5 (B) 1+ 25C5 + 25C7 (C) 1 + 25C7 (D) None of these



MATHEMATICS28. If two circle (x –1)2 + (y–3)2 = r2 and x2 + y2 – 8x + 2y + 8 = 0 intersect in two distinct points, then

(A) 2 < r < 8 (B) r < 2 (C) r = 2 (D) r > 2

29.xtan(lnx)tan ln tan(ln2)2 dx

x

is equal to ..... (c being arbitrary constant)

(A) ln sec(lnx) c

xsec(ln )2

(B) ln 2 tan(ln2)

sec(lnx) cxsec ln x2

(C) ln tan(lnx)xsec ln . x c

2

(D) ln tan (ln2)

sec(lnx) cxsec ln x2

30. If x1, x2,x3 are positive roots of the equation x3 – 6x2 + 3px – 2p = 0, p R then the value of

sin–1 1 2

1 1x x

+ cos–1

2 3

1 1x x

– tan–1

3 1

1 1x x

is equal to :

(A) 4

(B) 2

(C) 34

(D)




31. A particle retards from a velocity V0 while moving in a straight line. If the magnitude of deceleration is directlyproportional to the square root of the speed of the particle, then its average velocity for the total time of motionis :

(A) 3V2 0 (B) 3

V0 (C) 2V3 0 (D) None

32. A car negotiates a curve of radius R with constant speed V. Then the average force exerted by the ground onthe car over a time in which the car revolves through an angle is :

(A)

22mV sin2

5R

(B)

22mV sin2

3R

(C)

RmV2 2

(D)

22mV sin2

R

33. A small block of mass m is placed over a long plank of mass M. At t = 0, m is given a velocity V1 and M avelocity V2(>V1). After this M is given a constant acceleration (less than g). Coefficient of friction is between block and plank and ground is smooth. Then which is correct graph between velocity of block andtime :

Mm

V1

V2

a

(A)

t

v

(B)

t

v

(C)

t

v

(D)

t

v



PHYSICS


34. The graph of potential energy and position x is as shown. Assume that potential energy is depending on xonly. Also assume for x < – 10 and x > 15, U = 0.

155

25

50

–5–1010

x(m)

U(x)J

If the total mechanical energy is 25 J, then where can the particle be found(A) –10 < x < –5 and 6 < x < 15 (B) –10 < x < 0 and 6 < x < 10(C) –5 < x < 6 (D) None of these

35. A solid cube of side a and density d is floating in a liquid of density 3d. The cube is pressed down slightly andreleased. Find the time it would take in coming to original position.

(A) g3

a (B)

g3a

2 (C)

g3a2

(D) g3a2

2

36. Light of wavelength is incident on a slit. First minima of the diffraction pattern is found to lie at a distance of6mm from the central maximum on a screen placed at a distance of 2m from the slit. If slit width is 0.2 mm,then wavelength of the light used will be –(A) 4000Å (B) 6000Å (C) 7000Å (D) 7400Å


PHYSICS


37. A thermally insulated piece of metal is heated under atmospheric pressure by the source providing constantpower P, due to this its absolute temperature depends on time as T(t) = T0 [1 + K(t – t0)]1/4.Here K, t0 and T0 are constants. Then the heat capacity Cp(T) can be given by

(A) 0KT

P4(B) 4

0

3

KTPT4

(C) 40

3

KTPT2

(D) 0KT

P2

38. One mole of an ideal monoatomic gas undergoes thermodynamic cycle as shown. Initial temperature isT0 = 300 K. Take Process 1 2 : P = aV

Process 2 3 : PV = constant

Process 3 1 : P = constant ( n(3) = 1.09)Net work done by the cycle

2P

3

3V0V0 V

3P0

P01

(A) 3.27 RT0 (B) 6.83 RT0 (C) 4.53 RT0 (D) 5.81 RT0

39. A pulse started at a time t = 0 along the +x-direction on a long, taut string. The shape of the pulse at t = 0is given by function f(x) with

otherwise0

1x0for1x–

0x4–for14x

)x(f

f(x) and x are in centimeters. The linear mass density is 50 gm/m and it is under tension of 5N. The shapeof the string is drawn at t = 0, then the area enclosed by pulse and x-axis is :(A) 2 cm2 (B) 2.5 cm2 (C) 4 cm2 (D) 5 cm2


PHYSICS


40. A wave pulse starts propagating in the positive x-direction on a wire of length 10 m and linear mass density() given by = 0 + ax. The tension is 100 N. What is the time taken by pulse to go form x = 0 to x = 100 = 10–2 Kg/m and a = 9 × 10–3 Kg/m2

(A) 0.227 s (B) 0.454 (C) 0.113 (D) None of these

41. Four charges are placed on the circumference of a circle of radius R, 90° apart as shown in the fig. Theelectric field strength at the centre of the circle is

(A) 20

1 2 5Q4 R , making angle tan–12 with the – ve axis.

(B) 20

1 2 5Q4 R , making angle tan–12 with the + ve axis.

(C) 20

1 4 2Q4 R , making angle tan–1 1

2 with the – ve axis.

(D) 20

1 4 2Q4 R , making angle tan–1 1

2 with the + ve axis.

42. A charge of 10C is placed at the origin of (x-y) coordinate system. The potential difference between twopoints (a/2, a/2) and (a, 0) in volts is

(A) 9 104/a (B) 9 104/a2 (C) 9 104/2a (D) 0

43. An astronomical telescope has an objective of focal length 200 cm and an eyepiece of focal length 5 cm.What is the separation between the objective and the eyepiece and the magnifying power of the telescope,if eye is in relaxed state ?(A) 205 cm, 40 (B) 225 cm, 48 (C) 205 cm, 48 (D) None of these


PHYSICS


44. A self propelled vehicle of mass M = 1000 kg has engine which delivers constant power P = 7 kW.To increase the velocity of the vehicle from 10 m/s to 40 m/s distance travelled by it is n km. The value of n is(A) 6 (B) 3 (C) 9 (D) None of these

45. The figure shows the behavior of light rays w.r.t. a plano-convex lens whose plane surface is silvered. If therefractive index of the material of the lens 1.5 and the radius of curvature of the curved part of the lens is(5x) cm. Then the value of x is

30cm

(A) 3 (B) 1 (C) 2 (D) 4

46. The amount of heat given to the diatomic ideal gas is equal to the decrease in its internal energy. It is giventhen that the equation of process is PV(6/x) = constant. The value of x is :(A) 7 (B) 5 (C) 11 (D) 2


PHYSICS


47. A point object O is placed in front of a concave mirror of focal length 20 cm on the principal axis of theconcave mirror at a distance of 5 cm from the pole as shown in the figure. A glass slab is also placed in frontof the mirror, perpendicular to this principal axis. The image formed by the system for first reflection and thenrefraction is :

O5cm 5cm

P

=3/2t=3cm

Glass Slab

(A) Virtual behind the mirror. (B) Real between the mirror and the slab(C) Virtual between the mirror and the slab (D) Can’t be decided by above data.

48. An electron of mass me initially at rest, moves through a certain distance in a uniform electric field in time t1.A proton of mas mp also initially at rest, takes time t2 to move through an equal distance in this uniformelectric field. Neglecting the effect of gravity, the ratio t2/t1 is nearly equal to :

(A) 1 (B)

12

p

e

mm

(C)

12

e

p

mm

(D) 1836

49. A ray of light is incident at small angle i on a surface of a prism of small angle A & emerges normally fromthe opposite surface. If the refractive index of the material of the prism is , the angle of incidence i is nearlyequal to :(A) A/ (B) A/(2 ) (C) A (D) A/2


PHYSICS


50. Figure (a) and (b) show water drop and mercury drop in two identical conical glass pipes, then

(A) The water drop tends to move towards narrow end and mercury drop towards wide end.(B) The water drop tends to move towards wide end and mercury drop towards narrow end.(C) both tend to move towards wide end.(D) both tend to move towards narrow end.

51. A sliding fit cylindrical body of mass 1 kg drops vertically down at a constant velocity of 5 cm/s. Co-efficient

of viscosity of oil in 2msN

is :

1kg 15 cm

oil

15cm

14.9cm

(A) 1.4 (B) 1.9 (C) 0.7 (D) 2.8

52. The flow rate from a tap of diameter 1.25 cm is 3 litre/min, the coefficient of viscosity of water is 10–3 2msN

,

then reynolds number is :(A) 3095 (B) 1245 (C) 5095 (D) 1095


PHYSICS


53. Two soap bubbles of radii r1 and r2 coalesce to form a single bubble under isothermal condition. Which of thefollowing is radius of resulting bubble (Assume zero outside pressure)

(A) 21

21

rrr.r (B) |r1 – r2| (C) 2

221 rr (D) None

54. A container has two immiscible liquids of densities 1 and 2 (> 1). A capillary tube of radius r is inserted inthe liquid so that its bottom reaches upto the denser liquid. The denser liquid rises in the capillary and attainsa height h from the interface of the liquids, which is equal to the column lengths of the lighter liquid. Assumingangle of contact to be zero, the surface tension of heavier liquid is

1

2

h

(A) 2r2gh (B) 2rgh2

(C) 2 1

r ( )gh2 (D) 2pr(2 – 1)gh

55. A uniform vertical electric field E in upward direction is established in the space between two large parallelplates. A small conducting sphere of mass m is suspended in the field from a string of length L. If the spheresis given a positive charge q, the period of osicllation of this pendulum is (qE < mg)

(A) L2g

(B) L2

g (qE / m)

(C) L2

g (qE / m)

(D) 2 2 1/2

L2[g (qE / m) ]



PHYSICS56. An unpolarized beam of light has intensity I0. It is incident on to ideal polarizing sheets. The angle between

the axes of polarization of these sheets is . Find if the emerging light has intensity I0/4.

(A) sin–1

21

(B) sin–1

51

(C) sin–1

21

(D) cos–1

21

57. A light ray incident along vector ˆ ˆ ˆ2i 4 j 5k strikes on the x-z plane from medium I of refractive index 3

and enters into medium II of refractive index is 2. The value of 2 for which the value of angle of refractionbecomes 90º is

(A) 4 3

5(B)

3 35 (C)

2 35 (D) None of these

58. Figure shows variation of potential V with distance y from origin along y-axis. What is electric field at y = 2.5m & y = 5.5 m.

(A) ˆ3 j , ˆ5 j (B) ˆ2j , – ˆ5 j (C) ˆ3.5 j , ˆ2.5 j (D) ˆ3.5 j , – ˆ2.5 j



PHYSICS59. The lateral displacement of light passing through a parallel plate of glass of thickness t with angle of incidence

60º and angle of refraction 45º is

(A) t1–3 (B)

2t1–3

(C)

2t13

(D) None of the above

60. Four equal charges of magnitude q each are placed at four corners of a square with its centre at the originand lying in y-z plane. An external charge +Q is moved along x-axis. The electrostatic potential energy. Uvaries on x-axis as

(A)

U

–x xO

(B)

U

–x xO

(C)

U

–x xO

(D)

U

–x xO




61. If all carbon atoms of H2C = C = CH2 molecule lie at z-axis, then nodal plane of each -bonds does not lie inwhich of the following plane(A) XY (B) YZ (C) XZ (D) None of these

62. A system absorbed 20 kJ of heat and work done on the surrounding is 10 kJ. The change in internal energyis equal to (in kJ)(A) 10 (B) 30 (C) – 10 (D) 30

63. Which of the following are better leaving groups than CH3COO– ?(i) CH3O– (ii) CH3SO3

– (iii) CH3SO2– (iv) CF3SO3

–

(A) i (B) i, ii (C) i, ii, iii, iv (D) ii, iii, iv

64. Which of the following hydrate isomer of complex CrCl3.6H2O has higher wave length of absorption in thevisible region(A) [Cr(H2O)6]Cl3 (B) [CrCl(H2O)5]Cl2.H2O(C) [CrCl2(H2O)4]Cl.2H2O (D) [CrCl3(H2O)3].3H2O




CHEMISTRY65. How many dichlorination products (including stereoisomers) are possible for the following reaction?

Cl

Cl /h2

(A) 6 (B) 7 (C) 8 (D) 9

66. 10 mol of SO3(g) is heated from 400 K to 500 K according to a process which obey PV–1 = constant.The amount of heat absorbed by the system is (in kcal)(A) 4 (B) 7 (C) 8 (D) 9

67. EDTA4– does not form complex ion with(A) Al3+(aq) (B) Ca2+(aq) (C) Be2+(aq) (D) Mg2+(aq)

68. Identify the product of the following reaction sequence

OO

EtO OEt EtONa CH3I AA

(A) OO

(B) OO

EtO(C)

OO

EtO OEt(D)

OO

I I



CHEMISTRY69. 10 mol of an ideal gas [Cv,m (cal.K–1 mol–1) = 0.1 + 10–4 T] is heated in closed rigid vessel from 200K to 400K

temperature. H of the process is :(A) 3280 cal (B) 426 cal (C) 4260 cal (D) 260 cal

70. Incorrect order between borazine and benzene is(A) Reactivity towards HCl : B3N3H6 > C6H6

(B) C–H bond length in C6H6 > N–H bond length in B3N3H6(C) B–N bond length in B3N3H6 > C–C bond length C6H6

(D) C–H bond length in C6H6 > B–H bond length in B3N3H6

71. Consider the following reaction

HC CH Red hot Fe A AlCl3

O

Cl B,

Identify B :

(A)

Cl

(B)

O

Cl (C)

O

(D)

Cl

ClCl

72. The rate of a reaction increase 4 times when its temperature change from 300 K to 320 K. The activationenergy of such a reaction is equal to (ln 2 = 0.7)(A) 13.44 kcal (B) 6.72 kcal (C) 26.88 kcal (D) 3.36 kcal


CHEMISTRY


73. In which of the following compound each aluminium atom is surrounded by six other atoms in solid state(A) AlH3 (B) AlBr3 (C) AlI3 (D) All

74. Select all products that are formed upon reductive ozonolysis (in Zn/H2O) of 2,4-Dimethylpent-2-ene.

(A) O

(B) O

(C) O

(D) O

75. For nuclear reaction,

14 4 27 2 1N He X H , X is

(A) 168 O (B) 16

9 F (C) 188 O (C) 18

9 F

76. 20 ml, 0.1 M solution of complex compound CoBr2.NO3.H2O.3NH3 was treated with excess of AgNO3 solutionand 0.002 moles coloured precipitate was obtained. Then correct statement for the given complex compoundis(A) It exhibits hydrate isomerism(B) It exhibits linkage isomerism(C) It exhibits ionization isomerism(D) Secondary valency of metal cation is satisfied by both Br– ion



77. A 20 L steel jar containing He(g) at 10 atm is placed in a big vessel containing air at 1 atm and then sealedas following.

He(g)(10 atm)

air (1 atm)

Now He(g) is allowed to leak through a tiny hole into the jar. After long time, if a constant pressure of 2 atmis observed in the jar then the volume of big vessel is : (Assume temperature remains constant)(A) 200 L (B) 160 L (C) 180 L (D) None

78. Which of the following elements can be detected by lassaigne’s Test?(A) Carbon (B) Oxygen (C) Hydrogen (D) Phosphorus

79. 2 2x yd

orbital of inner shell is not used in the hybridization of :

(A) [Cu(NH3)4]2+ (B) [Ni(CN)5]

3– (C) Fe(CO)5 (D) None

80. At 298 K, one gram sample containing CH3COOH (Ka = 10–5) & some inert impurity is dissolved in waterand the solution is made upto 100 mL. If pH of resulting solution is 3 then % purity of sample is :(A) 30% (B) 60% (C) 40% (D) 70%


CHEMISTRY


81. OH Na

A Ph Br B , Identify B.

(A) Br (B) Ph O (C) OPh

(D) O Ph

82. Which of the following complex compound does not exhibit structural isomerism(A) [Pt(en)2][CuCl4] (B) [PtBrCl(en)2](C2O4) (C) [Pt(NO2)(en)2]

3+ (D) [Co(SCN)(H2O)5][NiCl4]

83. Identify the reactant for the synthesis of following compound by Oxymercuration Demercuration (OMDM).

OH

(A) (i) Hg(OAc) ,H O22

(ii) NaBH ,OH¯4(B)

(i) Hg(OAc) ,CH OH32

(ii) NaBH ,OH¯4

(C) BH ,THF3

H O,OH¯2(D)

(i) Hg(OAc) ,H O22

(ii) NaBH ,OH¯4

84. If number of orbitals present in the highest energy subshell of a shell are 5 then the maximum number ofelectrons having s = + 1/2 in this energy shell, will be :(A) 18 (B) 8 (C) 4 (D) 9



CHEMISTRY85. Incorrect order of stability of complexes.

(A) [Cu(trien)]2+ > [Cu(py)4]2+ (B) [Os(H2O)6]

3+ > [RuF6]3–

(C) [Ni(dmg)2] > [Ni(NH3)6]2+ (D) [Co(en)3]

3+ > [Co(CN)6]3–

86. Predict reaction mechanism and product of following reaction CH – C – Br3

CH3

CH3

EtOH

(A) SN1 , OEt (B) SN2 , EtO

(C) SN1, OH (D) SN2, HO

87. Calculate change in internal energy of gas when 2 moles of monoatomic gas is compressed reversibly andadiabatically from 16 L to 2 L at 300 K(A) 3600 cal (B) 2520 cal (C) 2700 cal (D) 5400 cal



CHEMISTRY88. When ferric alum, K2SO4.Fe2(SO4)3.24H2O, is added into excess of water, then colour shade of its aqueous

solution is found to be different from that of solid ferric alum. Colour change is due to the formation of(A) [Fe(H2O)4(OH)2] (B) [Fe(H2O)5(OH)]2+ (C) [Fe(H2O)6]

3+ (D) [K(H2O)6]+

89. Select the product of following reaction sequence

NO2

BrBr

KOH

(A)

OH

BrBr

(B)

NO2

BrOH

(C)

NO2

OHBr

(D)

OH

90. Calculate work done when 1 mole of A is reacted as per reaction A () + 3B(g) 2C(g), at 1 atm and 227°C(A) 1 J (B) 4.157 J (C) 8.314 J (D) None of these












C. Marking Scheme :



CODE - ADATE : 05-06-16




















CODE - A


DATE : 26-06-16

Vibrant Academy (I) Pvt. Ltd. "A-14(A)" Road No.1, Indraprastha Industrial Area, Kota (Raj.) Ph. 0744-2423406 [RT-4,P-1-A-2]


Single Correct Choice TypeThis section contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for itsanswer, out of which ONLY ONE is correct.

1. Let f(x) = 3x3 + bx2 + bx + 3 where b R. If x = 2 is a root of the equation f(x) = 0, then the value of

2xlim

)2x()1e( )x(f

is equal to :

(A) 29

(B) 27 (C) 4

27(D)

227

2. Let f : R R be a function defined by f(x) = 2x3 – 21x2 + 78x + 24. The number of integers in the solution setof x satisfying the inequality f(f(f(x) – 2x3)) f(f(2x3 – f(x))) is :(A) 3 (B) 4 (C) 5 (D) 6

3. The value of n

lim k 1n

24

k 1 k

1 k x n((x k)(k 1– x))dxn

is :

(A) 1 (B) 21

(C) – 21

(D) – 1



MATHEMATICS


4. Let f(x) =

0xife1

0x,1|x|ifx1x1

2

x1

If left hand derivative of f(x) at x = 0 is q and right hand derivative of f(x) at x = 0 is p, then(A) p exists, but q does not exist (B) q exists but p does not exist(C) p = q = 0 (D) p – q is a non zero finite quantity

5. Let nnn )62–5()625(E , n N. Then

(A) En + 1 = 10 En – En – 1 (B) En + 1 = 10 En + En – 1(C) En is divisible by 4 (D) En is divisible by 2n


MATHEMATICS




6. Two sides of a rhombus OABC lying in first quadrant are along the lines 3xy and 3xy . If the area of

rhombus is 2 sq. units (O origin). Then

(A) Length of side of rhombus is 2 (B) Length of side of rhombus is 2

(C) Length of longer diagonal is )13(2 (D) Length of longer diagonal is )12(3

7. If in triangle ABC, cos(sinB + sinC) = sinA, then

(A) 2 B Ccot cot cot2 2 2 (B) 2 B Ctan tan tan

2 2 2

(C) 2 B Ccot tan tan2 2 2 (D)

B C B – Ccos cos cos2 2

8. A circle S touches the line x + y = 2 at (1, 1) and cuts the circle x2 + y2 + 4x + 5y – 6 = 0 at P and Q. Then(A) If PQ is perpendicular to the line x + y = 2, then equation of circle S is 2x2 + 2y2 + 17x + 17y + 29 = 0(B) If PQ is perpendicular to the line x + y = 2, then equation of circle S is 2x2 + 2y2 – 17x – 17y + 30 = 0(C) PQ always passes through (6, – 4)(D) PQ always passes through (– 6, 4)


MATHEMATICS


9. Let

0xif0

0xif)x1(lnx1cos)x(f

2, then which of the following is(are) correct

(A) f '(x) is non differentiable at x = 0 (B) f(x) is differentiable at x = 0(C) f '(x) is continuous at x = 0 (D) f '(x) is discontinuous at x = 0

10. If b1–na

)3n2)(2n2)(1n2(1

0n

where a, b N, then(A) a + b = 5 (B) a + 2b = 8 (C) a – b = 0 (D) a3 + 2b = 12

11. Let E1 : x2 + 3k2 – 1 2k(2x – 1)

E2 : x2 – (2x – 1)k + k2 0

be two inequations, where k is a parameter, then(A) If k > 0, then every solution of E1 is a solution of E2(B) If k > 0, then every solution of E2 is a solution of E1

(C) If k (–1, 0), then every solution of E1 is a solution of E2(D) If k (–1, 0), then every solution of E2 is a solution of E1


MATHEMATICS


12. The value of lying in interval

2

,0 and satisfying 04sin41cossin

4sin4cos1sin4sin4cossin1

22

22

22

is(are)

(A) 247

(B) 2411

(C) 245

(D) 24

13. If dxx

xsinA0

, then the value of dxx

)bxcos()axsin(

0

must be

(A) A, if a > b > 0 (B) 2A, if a + b = 0

(C) ba

A

, if a > b > 0 (D) 0 if b > a > 0


MATHEMATICS


SECTION - IIIInteger Answer Type

This section contains 5 questions. The answer to each of the questions is a single-digit integer, ranging from0 to 9. The appropriate bubbles below the respective question numbers in the ORS have to be darkened. Forexample, if the correct answers to question numbers X, Y, Z and W (say) are 6, 0, 9 and 2, respectively, thenthe correct darkening of bubbles will look like the following :In all cases round answer to nearest integer value (if required)

0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

14. If

)x(f–1)x(f2logx 4 , then find f(2017) + f(–2016).

15. Let k

k , if k is oddP 1 , if k is even

k – 1

and N)2k(logP14

1k)1k(k

, then find the number of solutions of the equation

tan2x + cot2x + 2 = N sin22x for x [0, 2]


MATHEMATICS


16. If qp

)nn)(1nn()1n(n

1n224

223

, where p, q are relatively prime natural numbers, then find the value of p + q.

17. Let F(x) be a non negative continuous function defined on R such that 321xF)x(F

, x R.

Then the value of 1500

0

dx)x(F750

1 is

18. If the acute angle between the tangents drawn from (0, 1) to the graph of f(x) = x3 – 3x2 + 3x is

n2m3tan 1–

where m, n are relatively prime natural numbers. Then the value of |m – n| is




19. A point charge q = 6C is moving towards the centre of an earthed conducting sphere of radius R = 2m with aconstant velocity = 3m/s. Find the rate of flow of charge into the earth (in Coulomb per second), when q is at3 metres from centre of sphere.

q

(A) 8 (B) 4 (C) 12 (D) None of these

20. The reading of a barometer containing some air above the mercury column is 73 cm while that of a correctone is 76 cm. If the tube of the faulty barometer is pushed down into mercury until volume of air in it isreduced to half, then the reading shown by it will be :(A) 70cm (B) 72cm (C) 74cm (D) 76cm



PHYSICS


21. n identical charges, q each, are placed at the corners of a regular n-sided polygon of side a. One charge isreleased from its position. Repelled by others, when it has reached far away its kinetic energy is found to beE. A neighbouring charge is now released. When this second charge reaches far away its kinetic energy will

be 0

1K4

.

(A) E – a

Kq2

(B) E + a

Kq2

(C) E – a

Kqn

1n 2(D) E –

aKq

1n2n 2

22. A particle is moving in the xy-plane with the position as a function of time given by r (t) = j)t(yi)t(x .

The origin is at r 0

. The particle is definitely moving towards origin when

(A) vx > 0, vy > 0 (B) vx < 0, vy > 0 (C) xvx + yvy < 0 (D) xvx + yvy > 0

23. Water is flowing in a river at 2.0 m/s. The river is 50 m wide and has an average depth of 5.0 m. The poweravailable from the current in the river is (density of water = 1000 kg/m3) [MW = mega watt].(A) 0.5 MW (B) 1.0 MW (C) 1.5 MW (D) 2.0 MW


PHYSICS




24. A lens of focal length ‘f’ is placed in between an object and screen at a distance ‘D’. The lens forms two realimages of object on the screen for two of its different positions, a distance ‘x’ apart. The two real imageshave magnifications m1 and m2 respectively (m1 > m2).

(A) f = 21 mm

x (B) m1m2 = 1 (C) f =

D4xD 22

(D) D 4f

25. Two cars A and B are approaching each other as shown in figure.

A u1

a

Bu2

XO (X , 0)0

At t = 0, the velocities of A and B are u1 and u2 and they are at x = 0 and x = x0, respectively. The car A ismoving with constant velocity while B is moving with constant acceleration a, whose direction is shown.If xrel, urel and arel are displacement, velocity and acceleration of A w.r.t. B respectively, then mark out thecorrect options.

(A)

t

Slope = –au +u1 2

urel

(B)

t

Slope = au +u1 2

urel

(C)

t

xrel

(D)

t

arel

a


PHYSICS


26. Two coherent identical sound sources S1 and S2 (wavelength each) are kept at a distance 6 from eachother. Consider two circles C1 (radius 4) and C2 (radius 2) as shown in the figure.

C1

S1

C2

S2

(A) Number of places, where maxima will be observed on C2 is 8.(B) Number of places, where maxima will be observed on C1 is 8.(C) Number of places, where minima will be observed on C2 is 8.(D) All of the above.

27. A parallel beam of light ( = 5000 Å) is incident at an angle = 30º with the normal to the slit plane in aYoung’s double slit experiment. Assume that the intensity due to each slit at any point on the screen is I0.Point O is equidistant from S1 and S2. The distance between slits is 1 mm.(A) The intensity at O is 4I0.(B) The intensity at O is zero.(C) The intensity at a point on the screen 4mm from O is 4I0.

S1

O

S2

2m(D) The intensity at a point on the screen 4mm from O is zero.

28. Inside a uniform sphere of mass M (M is mass of complete sphere) and radius R, a cavity of radius R3 is

made in the sphere as shown.(A) Gravitatinal field inside the cavity is uniform.(B) Gravitational field inside the cavity is non-uniform.

(C) The escape velocity of a particle projected from A is 88GM45R

R

A

C

R/3 B

(D) Escape velocity is defined for the earth and particle system only.


PHYSICS


29. Mark the correct statement(s) for a very thin soap film (RI = 1.33) whose thickness is much less thanwavelength of visible light.(A) Film appears dark.(B) Film appears shiny.(C) Film on glass (RI = 1.5) appears dark.(D) Film on glass (RI = 1.5) appears shiny.

30. A coin is dropped in an accelerating rail road car. The path of the coin as observed from

a

(A) Ground frame of reference is parabola, if speed of the railroad car at the instant of dropping the coin iszero.(B) Ground frame of reference is parabola, if speed of the railroad car at the instant of dropping the coins isnon-zero.(C) Ground frame of reference is straight line, if speed of the railroad car at the instant of dropping the coin iszero.(D) Railroad car frame of reference is a straight line.

31. Let Vav , Vrms , VP respectively denote the mean speed, root mean speed and most probable speed of themolecules in an ideal monoatomic gas at absolute tmperature T. The mass of a molecule is m. Then

(A) No molecule can have a speed greater than 2 Vrms.

(B) No molecule can have a speed less than PV / 2 .

(C) VP < Vav < Vrms

(D) The average kinetic energy of a molecule is 2P

3 mv4





0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

32. A ray PO is incident on the mirror AC at angle 30º as shown in the figure. Ray PO is then reflected by mirrorAB and AC. The deviation of ray PO after its third reflection from mirror AC is k. Find the value of k.

30ºP

CO

30ºBA



PHYSICS33. The linear charge density on the circumference of a ring of radius R is = 0 sin, where is defined as

shown in figure. Then the electric dipole moment (in C-m) of the ring (if 0 = 1

C/m and R = 1m) will be :

x

y

34. A cavity of radius 'a' is cut from a non-conducting uniform positively charged sphere of radius '2a'. A negativecharged particle of mass m and charge q is released from point P(C, C' and P are collinear points) . Then thetime (in sec) taken by the charge particle to hit wall of cavity is, ( charge density of sphere and take

0m 1q 3

).

C'

C

PU=O


35. Consider the adjacent figure, a piston divides a cylindrical container into two parts. The left part contains 1mole of helium gas and the right part contains two moles of oxygen gas. the initial temperatures and pressures

of the gases in the left chamber are T0 and P0 and the right chamber are 0T2

and P0 respectively, as shown

in the figure. The piston as well as the walls of the container are adiabatic. After removal of the piston, gases

mix homogenously and the final pressure becomes p = 04n P13

. Find the value of n.

1 mole He, P , T0 0

2 mole O , 2

T0

2P0 ,

36. A ball is sliding on a 80 cm high horizontal table with a speed of 2 m/s. It falls off the table, hits the ground andbounces to a height of 45 cm as shown. The distance x is n2 cm. Find n (if coefficient of friction between balland ground is 0.2).

45cm

2m/s

80cm

x

x

y

PHYSICS





37. 3 mol of oxygen reacts with 4 mol of carbon completly to form CO and CO2. Which is correct statement?(A) Final composition is 50% by mass of CO2.(B) Vapour density of final gaseous mixture is 36(C) Relative density of gaseous mixture w.r.t. Helium is 9(D) Density of gaseous mixture at 0.821 atm pressure and 360ºC temperature is 1g/litre

38. Which order is CORRECT for (splitting energy) and INCORRECT for stability(A) K3[Co(CN)6] > [Co(en)3] Cl3(B) K3[Cr(NO2)6] > K3[Cr(C2O4)3](C) K3[Fe(CN)6] > K4[Fe(CN)6](D) K[Ag(CN)2] > K[Au(CN)2]



CHEMISTRY


39.O O

H O318

Identify product

(A) OH

CH=OOH

1818

(B) OH

CH=OOH

18 (C) OH

OOH

(D) OH

CH=O CH=O

40. Which non-magnetic ore contain magnetic impurity(A) Tin stone (B) Haematite (C) Pyrolusite (D) Chromite

41. An ideal gas [Cv,m (cal.mol–1K–1) = 2 + 10–2 T] is heated from 200 K to 400 K under constant volume.The change in molar entropy of gas is equal to (in cal K–1mol–1).[Given : ln2 = 0.7](A) 1.4 (B) 2.4 (C) 3.4 (D) 4.8


CHEMISTRY




42. Given : A(g) + 2B(g) C(g), rCp = 0fH0 (C, g) = –200 kJ mol–1 fH0 (B, g) = –20 kJ mol–1 , fH0 (A, g) = –120 kJ mol–1

0mS (C, g) = 250 J mol–1K–1 , 0

mS (B, g) = 30 J mol–1K–1 , 0mS (A, g) = 200 J mol–1K–1

All data at 400 K temperature. Which is/are correct statement(s) ?(A) Change in entropy of reaction at 400 K is – 10JK–1

(B) Change in enthalpy of reaction at 400 K is –40kJ(C) Change in entropy of surrounding at 400 K is 100 JK–1

(D) Change in free energy of reaction is 35 kJ at 500K

43. In which of the compound cationic rearrangement possible, whenever treated with Conc.H2SO4.

(A)

O

(B) OH

(C) OH

(D) OH

44. Select CORRECT statement for Cu2[Fe(CN)6](A) It is coloured compound (B) Colour obtained due to metal to metal charge transfer(C) It is paramagnetic species (D) t2g orbitals are used in hybridization


CHEMISTRY


45. Br2

CCl4A

Reaction-(1)

H BrH Br

CH3

CH3

; dil.KMnO4A Reaction-(2)H OH

HO H

CH3

CH3

HO HH OH

CH3

CH3

Correct statement about the both reaction.(A) Reaction-1 is regioselectivity reaction. (B) Reaction-1 is stereoselective reaction.(C) Reaction-2 is stereoselective reaction. (D) Reaction-2 is stereospecific reaction.

46. The solubility of AgCl(s) in water is 10–5 mol litre–1. Which is/are correct statement(s)?(A) Solubility of AgCl(s) in NH3(aq) is greater than 10–5 mol litre–1

(B) Solubility of AgCl(s) in 0.1M AgNO3(aq) is 10–9 mol litre–1

(C) Solubility of AgCl(s) in 0.1M KCl(aq) is 10–4 mol litre–1

(D) Greater number of moles AgCl(s) dissolve in water on dilution

47. Which group of compound does not have same order of boiling point and melting point

(A)

ClCl

Cl Cl

ClCl

, , (B)

OHOH

,

OH

OH

(C) cis but-2-ene, trans but-2-ene (D) NH3, H2O, HF


CHEMISTRY


48. Which is/are INCORRECT process

(A) Bauxite ntdisplacememetalleaching Al (impure)

(B) Galena Calcination Carbon reduction Pb (impure)

(C) Copper glance Partial roasting Self reduction Cu (impure)

(D) Cinnabar Complete roasting thermal decomposition Hg (impure)

49. Consider following curve for electron of H-atom

r

4r

2 .R( r)2

The orbital(s) belonging to above curve can also be described by curve(s) :

(A) r

R( r

)2

(B) r

R(r

)

(C) r

R(r

)

(D)

r

R(r)


CHEMISTRY


SECTION - IIIInteger Answer Type


0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

50. Find total number of ligands which form diamagnetic homoleptic octahedral complex with Co3+ cation butform paramagnetic homoleptic octahedral complex with Fe2+ cation.

NH3, NCS–, NO2–, NO3

–, C2O42–, CH3COO–, H2O, F–, en

51. One mole of an ideal gas ( = 1.5) compressed adiabatically from (8.0L, 400K) to 4.0 L against constantexternal pressure of 8.314 bar. Calculate the value of 10 times of (S)total (in cal/K) for the process.(Given : ln2 = 0.7, ln3 = 1.1)



CHEMISTRY

52.NH

Number of CH3 – I consumed during the following reaction. In which Hoffmann exhaustive elimination takeplace.

53. xHIO

O O Ethyl iodide

Total number of HI consumed in the [9]-crown-[3] ether.

54. In order to determine the volume of blood in an animal a 10 ml of solution having an activity of 2.02 × 103 dpm

of 31 H is injected into the animal blood stream. After sufficient time for circulatory equilibrium to be estab-

lished, 5 ml of blood is found to have an activity equal to 10 dpm.Calculate the volume of blood (in litre) in animal.











CODE - ADATE : 26-06-16



10. Section I contains 5 multiple choice questions. Each question has 4 choices (A),(B), (C) and (D) for its answer, out of which only one is correct.


12. Section III contains 5 questions. The answer to each of the questions is aninteger, ranging from 0 to 9. The answer will have to be appropriately bubbled in theORS as per the instructions given at the beginning of the section.

C. Marking Scheme :

13. For each question in Section-I, you will be awarded 3 marks if you have darkenedonly the bubble corresponding to the correct answer and zero mark if no bubbles aredarkened. In all other cases, minus one (–1) mark will be awarded.

14. For each question in Section-II, you will be awarded 4 marks if you have darkenedonly the bubble corresponding to the correct answer and zero mark if no bubbles aredarkened. In all other cases, minus two (–2) mark will be awarded.Partical Marks : +1 For darkening a bubble corresponding to each correctoption, provided NO incorrect option is darkened.

For example, if (A), (C) and (D) are all the correct options for a question, darkeningall these three will result in +4 marks, darkening only (A) and (D) will result in +2marks, and darkening (A) and (B) will result in –2 marks, as a wrong option is alsodarkened.

15. For each question in Section-III, you will be awarded 3 marks if you darken thebubble corresponding to the correct answer and zero mark if no bubbles is darkened.No negative marks will be awarded for in this Section.




















CODE - A


DATE : 26-06-16




1. The value of

1n

2

!nn

equals

(A) e (B) e2 (C) 2e (D)

2. If the roots of the equation 10x3 – Kx2 – 54x – 27 = 0 are in Harmonic Progression (HP), then K is equal to(A) 3 (B) 6 (C) 9 (D) 12

3. The value of nLim

1–n41....

5n21

3n21

1n21

is :

(A) 2n21 (B) 3n

21 (C) 2n

31 (D) 3n

31



MATHEMATICS


4. If n8 3 7 = P + F . where P is an integer and F is fractional part, then

(A) P is an odd integer (B) P is an even integer(C) F(P + F) = 1 (D) None of these

5.x

3 4x 00

1 t.ln(1 t)lim dtx t 4

is equal to

(A) 13 (B)

14

(C) 16 (D)

112

6. The number of non-negative integral solutions of the equation x + y + 3z = 33, is(A) 120 (B) 135 (C) 210 (D) 520


MATHEMATICS




7. dxee1

1–

x–x 33

is less than

(A) 2 (B) e2e2 (C) 2

e1e (D) 2e

8. Let ),0(xdttsin1e)x(f2x

0

x1– 2

then which of the following statement(s) is/are correct

(A) f '(x) exists and is continuous for x (0, )(B) f "(x) exists for x (0, )(C) f '(x) is bounded(D) There exists > 0 such that |f(x)| > |f '(x)| x (, )

9. If the lines 2x – y = 8, x – 2y = 17 and line L = 0 form an isoceles triangle, then slope of line L can be

(A) 1 (B) 211– (C) –1 (D)

112–


MATHEMATICS


10. If dx)xcosx(sinx2/

0

nn

(A) 2002–101

99

101

(B) 62

–4

2

4

(C) 62

–101

99

101

(D) 82

–4

2

4

11. For the curve y = cx/a , which of the following is/are true(A) length of subtengent is constant(B) subnormal varies as the square of ordinate(C) eqaution of normal where curve cuts y-axis is cy + ax = c2

(D) subnormal varies as the square of obssussa

12. The circles x2 + y2 + 2x + 4y – 20 = 0 and x2 + y2 + 6x – 8y + 10 = 0, Then these two circles are(A) orthogonal(B) such that number of common tangents are 2

(C) such that length of common tangent is 1/4125

5

(D) such that length of common chord is 1/235

2


MATHEMATICS


13. Let 12cos2

)1–2cos2(·).....1–4cos2(·)1–2cos2(·)1–cos2()(f n

1–n

, where n N and

22m3

,

m , then

(A) 21

3f

(B) Let )x(f1)x(g then 2

x))x(gln(lim

2x

(C) 2–

2–x

)x(f)x(f–1sin

lim2

x

(D) Range of f(x) is (–, –1]

,31

14. Let dt)t(f·x1)x(f1

1–

2 , then

(A) 1

1–

2dx)x(f

(B) f(x) form a triangle of area

121

with axes

(C) Curve f(x) touches parabola : y2 = 24x at only one point(D) Curve f(x) touches parabola x2 = 4y at only one point


MATHEMATICS




Paragraph for Question Nos. 15 to 16

Let dt)at–t4()x(fx

0

34 and g(x) be a quadratic polynomial satisfying g(0) + 6 = g'(0) – c = g"(0) + 2b = 0,

where a, b, c are positive real numbers. If y = g(x) and y = f '(x) intersects in 4 distinct points with abscissae

xi, i = 1, 2, 3, 4 such that 8xi4

1i i

; then

15. Abscissae of point of intersection are in(A) Arithmatic progression (B) Geometric progression(C) Harmonic progression (D) None of these

16. The value of 'a' equals(A) 6 (B) 8 (C) 20 (D) 12



MATHEMATICSParagraph for Question Nos. 17 to 18

Consider a function f(n) = 2n11

Let n = n1

n

1r nrf and n =

1–n

0r nrf

n1

for n = 1, 2, 3......

17. Which of the following relation between n and n holds good for finite n ?(A) n = n (B) n < n(C) n > n (D) None

18. Which of the following inequality is true ?

(A) n < n < 4

(B) n > n > 4

(C) n > n4

(D) n < n4




19. A point charge q is placed at P(0, 0, a). The electric flux through area CAB due to electric field of q is . Then

A(0, a, 0)

P(0, 0, a)

(a, 0, 0)

z

y

x

O

q

B C(a,a,0)

(A) = 048

q (B) <

048q (C)

048q < <

024q (D) >

024q

20. Two particles are projected horizontally in opposite directions from a point in a smooth inclined plane ofinclination with the horizontal as shown in figure. Find the separation between the particles in the inclinedplane when their velocity becomes perpendicular is :

v2

v1

(A)

singvv)vv( 2121

(B) singvv)v–v( 2121

(C)

cosgvv)vv( 2121

(D) gvv)vv( 2121



PHYSICS


21. A car of mass m = 1000 kg is moving very slowly on a parabolic shaped bridge AFOE of span m40 and

height h = 20m as shown in the figure. Then the net force applied by the bridge on the car when the car is atpoint F, is :

O

h

C DBA10m E

F

(A) 5000 N25

(B) N2

5000(C) 10000 N (D) N

525000

22. A block B is suspended from a cable that is attached to the block at E, wraped around three pulleys and istied to the back of a truck D. The truck starts from rest when all cables are vertical and moves forward witha constant acceleration of ap = 3/2 m/s2 the speed of the block at the instant when truck has moved 3 metersis (Assume block B remains always horizontal) :

A

B

4m

E

(A) s/m51

(B) s/m52

(C) s/m53

(D) 1 m/s


PHYSICS


23. A metallic plate having shape of square is suspended as shown in figure. The plate is made to dip in watersuch that level of water is well above that of the plate. The point X is then slowly raised at constant velocitythen curve between tension T in string and displacement S of point X is given by

x

(A) S

T (B) S

T (C) S

T (D) S

T

24. A non-conducting rod AB having uniformly distributed positive charge of linear charge density is kept inx–y plane. The rod AB is inclined at an angle 30º with positive y-axis. The magnitude of electrosatic field atorigin due to rod AB is E0 N/C and its direction is along line OC. If line OC makes and angle = (10 a + b)degree [where a and b are the positive interger less than 9] with negative x-axis, as shown in the figure,then the value of (a + b) [OB = 2m and = 10–3C/M].

C

x'

y'

O

A

Bx

y

+

+

30º



PHYSICS




25. An object is moving on principle axis in front of a spherical mirror, m is instantanceous transverse magnification.The velocity of object is constant. Mirror is stationary. v and a are velocity and acceleration of imagerespectively. The correct statement(s) are :(A) v m2 (B) v m (C) a m3 (D) a m4

26. P1 and P2 are identical prisms arranged as shown in figure. A ray of white light incident on face of P1

undergoes dispersion and falls on one face of P1 undergoes dispersion and falls on one face of P2. The facingsurfaces of the prisms are parallel to each other and separation between them is negligible. Then.

Red

Violet

P2

A

A

P1White

(A) Light emerging from P2 will be white(B) In the light emerging from P2, dispersion will be greater.(C) The direction of light emerging from P2 will be parallel to the direction of ray incident on P1

(D) The ray emerging from P2 will be white even if prisms P1 and P2 have identical geometry but differentmaterial.


PHYSICS


27. Three liquid baths are thermally connected with the help of two identical rods AB and CD, each havingthermal resistance 1ºC/W. There is a heater of 100 W in the middle bath; The temperature of the left handliquid bath is maintained at 100ºC and that of right hand side is maintained at 40ºC. Assume there is no heatloss in surrounding.

A B C Dheater

(A) The steady temperature of the middle bath will be 120ºC.(B) The heat current in the left hand side rod is 20W.(C) The heat current in the right hand side rod is 65W.(D) The heat current in the right-hand side rod is towards right.

28. In the adjacent figure there is a cube having a smooth groove at an inclindation of 30º with horizontal in itsvertical face. A cylinder A of mass 2kg can slide freely inside the grove. The cube is moving with constanthorizontal acceleration a0 parallel to the shown face, so that the slider A does not have acceleration alonghorizontal.(A) The noraml reaction acting on slider A is zero

(B) The value of a0 is g 3 A

30º

a0

(C) The value of a0 is g(D) Acceleration of the slider A in ground frame is g.

29. An image of a bright square is obtained on a screen with the aid of a convergent lens. The distance betweenthe sauare and the lens is 40 cm. The area of the image is nine time larger than that of the square. Selectthe correct statement(s) (Plane of square is perpendicular to the principle axis).(A) Image is formed at a distance 120 cm from lens(B) Image is formed at a distance 360 cm from lens(C) Focal length of lens is 30 cm(D) Focal length of lens is 36 cm.


PHYSICS


30. Two spherical bodies of equal mass m rotate about their centre of mass in circular orbits. The distancebetween the centres of the two is r. Select the correct alternative(s) :(A) The KE of each is Gm2/4r(B) The angular momentum of each about centre of mass is

2rGm

21 3

(C) The KE of each is Gm2/2r

(D) The angular momentum of each about centre of mass is rGm3

31. Imagine that a dipole is at the centre of a spherical non conducting surface. If magnitude of electric field at acertain point on the surface of sphere is 10 N/C, then which of the following cannot be the magnitude ofelectric field anywhere on the surface of sphere(A) 4 N/C (B) 8 N/C (C) 16 N/C (D) 32 N/C

32. The maximum thickness of a plano convex lens, when viewed normally through the plane surface, appears tobe 6 cm and when viewed normally through the curved surface appears to be 7.2 cm. The actual maximumthickness is 9 cm. Then(A) the radius of curvature of lens is 18 cm(B) the refractive index of material of lens is 1.5(C) Light parallel to principle axis converges at 22 cm from curved surface when its plane surface is silvered.(D) Light parallel to principle axis converges at 8 cm from plane surface when its curved surface is silvered.


PHYSICS





A uniform cylindrical block of mass 2M and cross sectional area A remains partially submerged in a non-

viscous liquid of density , density of the material of the cylinder is 3. The cylinder is connected to lower end

of the tank by means of a light spring of spring constant K. The other end of the cylinder is connected to

another block of mass M by means of a light inextensible string as shown in the figure. The pulleys shown

are massless and frictionless and assume that the cross section of the cylinder is very small in comparison

to that of tank. Under equilibrium condition. half of the cylinder is submerged. [given K > 8Ag]

M2M

K

33. Under equilibrium condition

(A) extension of the spring is Mg3K (B) Compression of the spring is

2Mg3K

(C) Compression of the spring is Mg6K (D) extension of the spring is

Mg6K

34. By what maximum distance cylinder will be pushed downward into the liquid from equilibrium position, Sothat when it is set free then tension in the string will not vanish [Assume equilibrium position to be at rest]

(A) 3Mg

(K A g) (B) 3Mg

2(K A g) (C) 8Mg

3(K A g) (D) 3Mg

(2K 3A g)


Paragraph for Question Nos. 35 to 364 moles of an ideal gas is initially in a state A having pressure 2 × 105 N/m2 and temperature 200 K. Keeping

pressure constant the gas is taken to state B at temperature of 400 K. The gas is then taken to a state C in

such a way that its temperature increases and volume decreases. Also from B to C, the magnitude of dTdV

increases. The volume of gas at state C is equal to its volume at state A. Now gas is taken to initial state A

keeping volume constant. A total of 1000 J of heat is with drawn from the sample in the cyclic process. Take

R = 8.3 J/K/mol.35. Which graph between T and volume V for the cyclic process is correct ?

(A) A

400K

200K

T

V

B

C

(B) A

400K

200KT

V

BC

(C) A

400K

200K

T

V

B

C

(D)

400K

200K

T

VA

B

C

36. The work done in path B to C is :(A) 1000 J (B) –1000 J (C) –7640 J (D) 5640 J

PHYSICS





37. Which complex has maximum number of extra pairs of electrons due to crystal field splitting(A) [Co(NH3)6]

2+ (B) [Cr(en)3]2+ (C) [Pt(NH3)6]

4+ (D) Cr(CO)6

38. At 27ºC, 10 mole of a non-ideal gas present in high pressure range is gradually compressed from 2.5 dm3 to1 dm3 isothermally. If van-der waal constant ‘b’ of gas is 0.05 dm3mol–1 then the work done on the gas will be(Given : ln2 = 0.7 ; ln5 = 1.6)(A) 0.84 kcal (B) 9.6 kcal (C) 35.1 kcal (D) 8.4 kcal

39.I

Br

Cl

F

What is the exact value of (actual possible number of stereoisomers/theoratically possible number ofstereoisomers)?(A) 1/8 (B) 2/8 (C) 1/16 (D) 2/16



CHEMISTRY


40. Which complex has higher number of optical isomers in comparison of geometrical isomers(A) [Pt(gly)3]

+ (B) [Pt(en)(H2O)4]4+ (C) [Cr(NH3)3(H2O)3]

3+ (D) [Cr(NH3)4Cl2]+

41. For reaction : A kf

kb B ; H = 5 kcal/mol

rate constant (kf) is given as : nkf = 30 – T

7500 ,

where T is kelvin temperature then the value of activation energy for reverse reaction will be :(Given : R = 2 cal mol–1 K–1)(A) 2.5 kcal (B) 7.5 kcal (C) 15 kcal (D) 10 kcal

42.Cl/AlCl3

(i)

(ii) KMnO /H , 4+

(i) SOCl

(ii) H /Pd-BaSO2

2 4 Product is

(A)

CHO

(B)

COOH

(C)

CH –OH2

(D)


CHEMISTRY




43. All isomeric 2°-Alcohol (C5H12O) are dehydrated by conc. H2SO4/ and undergone ozonlysis. Identify theproducts possible?

(A) CH3–CHO (B) CH3–CH2–CHO (C) CH –C–CH3 3

O(D) CH –CH –C–CH3 2 3

O

44. One mol of non linear ideal gas is compressed isothermally and irreversibly in two stage compression.Stage-1 (2 bar, 200 L)Stage-2 (5 bar, 80L)Stage-3 (10 bar, 40L)Which is/are correct statement(s) ?(A) Change in enthalpy in process is zero.(B) Change in entropy in process is positive.(C) Total heat released in process is 100 kJ.(D) Work done on the gas is 100 kJ.

45. Which of the following combination of gerade atomic orbitals form gerade molecular orbitals.

(A)

–

–

++

–

–

++ (B)

+

+

–

–

+

+

–

–(C)

–

+

+

–(D)

+

–

+

–


CHEMISTRY


46. (I) (II) (III) (IV)

Which of the reactant is optically active product formed after reductive ozonolysis.(A) I (B) II (C) III (D) IV

47. 10 mol of an ideal gas ( = 1.5) behave as working substance in an engine working in a cycle as shown below.

D

C

B A

12VVV

P

The process AB, BC, CD and DA are respectively reversible isobaric, reversible adiabatic, reversible isochoricand reversible isothermal. The ratio of maximum to minimum temperature is 3. If maximum temperature is600K. Which is/are correct statement(s) about BC process ?(A) Change in enthalpy is 12 kcal (B) Change in entropy of gas is zero(C) Change in internal energy is 8 kcal (D) Work done on the gas is 8 kcal

48. Which property of alcohols is explained by H-bonding(A) Alcohols are more water soluble in comparison of ether, aldehyde, alkane, ketone with almost samemolecular mass(B) Alcohol has higher boiling point in comparision of 1º amine with almost same molecular mass(C) Alcohol are more water soluble than phenol(D) Among isomeric alcohols, 1º alcohol has highest boiling point


CHEMISTRY


49. Identify the compound/s more reactive towards SN–Ar (Nucleophilic Aromatic Substitution) than given compound.Br

NO2

(A)

BrNO2

NO2

(B)

Br

NO2

NO2

(C)

F

NO2

(D)

Br

NO2

50. fGº for the formation of n-butane is –15.69 kJ mol–1 and for isobutane is –21.39 kJ mol–1.Select correct statement(s) for the conversion of n-butane to isobutane if 100 mole of n-butane were takeninitially.[Given : 2.303 RT = 5.7 kJ/mol at 298 K](A) At the start of reaction, conversion is spontaneous(B) rGº is 37.08 kJ/mol(C) Equilibrium constant is 10(D) Mole fraction of isobutane in equilibrium mixture is 0.91


CHEMISTRY





A water insoluble compond 'P' on heating gives Q, R, S. and 'Q' is also water insoluble and changes colour

on heating. R & S are gaseous compounds where boiling point of R > S.

51. Compound 'P' is(A) PbC2O4 (B) ZnSO4 (C) FeSO4 (D) BeC2O4

52. Which pair of metals can form stable mononuclear neutral complex with gas 'S'(A) Cr, Fe (B) Cr, Mn (C) Mn, Co (D) Fe, Co


CHEMISTRY



CH = CH2

C

CH

NaNH2

(1 mol) (A)

CH – 3 I(1 mole) (B)

Br2

(1 mole) (C)

H2

Pd-BaSO4 (D)

53. Compound B is :

(A)

CH = CH – CH3

C

C Na

(B)

CH – CH2

C

CH

Br Br

(C) CH = CH2

C

C

Me

(D)

54. Compound D is :

(A) (B) CH – CH2

C

C

Br Br

Me

(C)

BrBr

(D) C C–CH 3











CODE - A





12. Section III contains 2 groups of questions. Each groups has 2 questions based on aparagraph. Each question has 4 choices (A), (B), (C) and (D) for its answer, out ofwhich one or more is/are correct.

C. Marking Scheme :


14. For each question in Section-II, you will be awarded 4 marks if you have darkenedonly the bubble corresponding to the correct answer and zero mark if no bubbles aredarkened. In all other cases, minus two (–2) mark will be awarded.Partical Marks : +1 For darkening a bubble corresponding to each correctoption, provided NO incorrect option is darkened.

For example, if (A), (C) and (D) are all the correct options for a question, darkeningall these three will result in +4 marks, darkening only (A) and (D) will result in +2marks, and darkening (A) and (B) will result in –2 marks, as a wrong option is alsodarkened.

15. For each question in Section-III, you will be awarded 3 marks if you darken thebubble corresponding to the correct answer and zero mark if no bubbles is darkened.No negative marks will be awarded for in this Section.

DATE : 26-06-16




















CODE - A


DATE : 31-07-16




1. Consider two quadratic expressions f(x) = ax2 + bx + c and g(x) = ax2 + px + q, (b p) such that the

discriminants are equal. If f(x) = g(x) has a root x = , then :(A) is the A.M. of the roots of f(x) = 0 and g(x) = 0(B) is the G.M. of the roots of f(x) = 0 and g(x) = 0(C) is the H.M. of the roots of f(x) = 0 and g(x) = 0(D) None of these

2. If I1 =

3

0

dx

21x

xsin and I2 =

0

3–21x

xsin dx , (where [.] represent greatest integral part), then

(A) I1 = 3I2 (B) I2 = 3I1 (C) I1 + I2 = 0 (D) I1 = I2

3. If a, b, c, d R such that 034

d3bc2a

, then the equation ax3 + bx2 + cx + d = 0 has

(A) atleast one root is (–1, 0) (B) atleast one root in (0, 1)(C) no root in (–1, 1) (D) no root in (0, 2)

4. If > are roots of x2 + kx – 1 = 0, then

(A) tan–1– tan–1= – 2

(B) tan–1 + tan–1 = –2

(C) tan–1 – tan–1 = 2

(D) tan–1 + tan–1 = 2




MATHEMATICS5. If 2sec2= tan+ cot, then the value of + can be :

(A) n – 4

(B) n + 4

(C) n – 2

(D) n + 4

3

6. A right angle triangle ABC having right angle at C, CA = a, CB = b moves such that the angular pointsA and B slides along x-axis and y-axis respectively. Then the locus of C is :(A) ax + by + 1 = 0 (B) ax ± by = 0(C) ax2 ± 2by + y2 = 0 (D) none of these

7. The value of404C4 – 4C1 . 303C4 + 4C2 . 202C4 – 4C3 . 101C4 is equal to(A) 0 (B) (101)4 (C) (201)4 (D) (401)4

8. The range of f(x) = x

xsin + xtan

x in

2,0 is :

(A)

2,2(B)

2,1(C) (0, ) (D) (2, )



MATHEMATICS9. A six letters word is formed using the letters of the word ALMIGHTY with or without repetition. The number of

words that contain exactly three different letters, is :(A) 15600 (B) 30240 (C) 8P6

– 8P3 (D) 13270

10. If

xtan2ax2 If x af(x) a

k If x a

, then value of k for which f(x) becomes continuous at x = a.

(A) 2 (B)

2

(C) 2e

(D) 2

e

11. If I =

15

8

dx(x – 3) x 1 ; then I equals.

(A) 1 5log2 3

(B) 52log3

(C) 1 log32

(D) 2 log3

12. The value of the integral 100

0

2 1– cos2x

dx is :

(A) 0 (B) 200 (C) 400 (D) 400



MATHEMATICS

13. If I = a x a – xa – x a x

dx, then I equals to :

(A) 2sin–1(x/a) + C (B) 2asin–1(x/a) + C (C) 2cos–1(x/a) + C (D) 2acos–1 (x/a) + C

14. If f(9) = 9 and f ’(9) = 4 ; then

x 9

f(x) – 3Lt

x – 3 is equal to :

(A) 3 (B) 4 (C) 5 (D) 9

15. If y = x – xe e then xy2 + 12

y1 is equal to :

(A) y (B) xy (C) y4

(D) x y

16. The tangent to the curve x = a cos2 .cos ; y a cos2 .sin at the point corresponding to = /6 is :

(A) Parallel to x-axis (B) Parallel to y-axis(C) Parallel to line y = x (D) None of these



MATHEMATICS17. The minimum value of f(x) = |3 – x| + |2 + x| + |5 – x| is :

(A) 0 (B) 7 (C) 8 (D) 10

18. The degree of the differential equation

22 3 22

2 3 2d y dy d y d y2 3 5 (x 2)log

dxdx dx dx

is


19. The degree and order of the differential equations of all parabolas whose axis is x-axis is :(A) 2, 1 (B) 1, 2 (C) 3, 2 (D) None of these

20. sin–1x + sin–1y = 23

and cos–1x – cos–1y = 3

, then (x + y) equals.

(A) 12

(B) 1 (C) 32

(D) None of these



MATHEMATICS

21. If I = sinx – cos x

sin2x dx, then I equals to :

(A) log |sinx – cosx + sin2x | + C (B) log |sinx + cosx – sin2x | + C

(C) log |sinx + cosx| + C (D) log |sinx – cosx| + C

22. If xcos= ycos

32

= zcos

34 , then the value of xy + yz + zx is equal to :

(A) 1 (B) 0 (C)

cos3cos

(D) 3cos

23. If the altitude, angle bisector and median drawn from the vertex A of ABC divide angle A in 4 equal parts.The measure of angle A is :(A) 60º (B) 90º (C) 120º (D) 150º

24. The equation tan4x – 2sec2x + a2 = 0 will have atleast one solution, if

(A) |a| 2 (B) |a| 4 (C) |a| 3 (D) |a| 1


MATHEMATICS


25. Total number of solution(s) of the equation |4sinx| – x2 + 2x = 1 is/are(A) 3 (B) 6 (C) 7 (D) None of these

26. If the expression a2(b2 – c2)x2 + b2(c2 – a2)x + c2(a2 – b2) is a perfect square of one degree polynomial of x,then a2, b2, c2 are in(A) A.P. (B) G.P. (C) H.P. (D) None of these

27. The number of integral points inside the triangle made by the line 3x + 4y – 12 = 0 with the co-ordinate axeswhich are equidistant from atleast two sides is/are (an integral point is a point both of whose co-ordinates areintegers) :(A) 1 (B) 2 (C) 3 (D) 4



MATHEMATICS

28. If a a

1 11–log x 1–log yy a , z a and x = ak, then k =

(A) a

11–log za (B)

a

11 log z (C)

z

11 log a (D)

z

11 log a

29. For an increasing A.P. a1, a2, ......., an if a1 + a3 + a5 = –12 and a1 . a3 . a5 = 80,then which of the followingis incorrect ?(A) a1 = –10 (B) a2 = –1 (C) a3 = –4 (D) a5 = 2

30. If n N, then n

nr

r 11 c .sin(n 2r)

is always

(A) positive (B) negative (C) non-positive (D) cannot be determined




31. An aeroplane is rising vertically with acceleration f. Two stones are dropped from it at an interval of time t.The distance between them at time t after the second stone is dropped will be

(A) 1(g f)tt2

(B) 1 (g f)(t 2t )t2

(C) 21(g f)(t t )2

(D) 21(g f)(t t )2

32. A cylinder and a wedge each of mass mare touching each other. Both are free to move on smooth inclinedsurfaces of two fixed inclined planes. The normal exerted by the wedge on the cylinder will be

fixedfixed

(A) 2mgtan (B) mgtan (C) 2mgcos (D) mgcos

33. A body of mass m starting from rest moves with acceleration proportional to cube root of its velocity. Theinstantaneous power delivered to the body is varying with time as

(A) t2 (B) t2/3 (C) t4/3 (D) t9/8

34. A small ball thrown at an initial velocity u directed at an angle = 37° above the horizontal collides inelastically(e = 1/4) with a vertical massive wall moving with a uniform horizontal velocity u/5 towards ball. After collisionwith the wall, the ball returns to the point from where it was thrown. Neglect friction between ball and wall. Thetime t from beginning of motion of the ball till the moment of its impact with the wall is (tan37° = 3/4)

(A) 3u5g (B)

18u25g (C)

54u125g (D)

54u25g



PHYSICS


35. A smooth rod OP is fixed vertically. A disc of mass m and radius R is rolling without slipping on a roughhorizontal surface as shown. Velocity of centre of mass of disc is v0. A rod AB of length L is connected withdisc at A, R/2 distance vertically up from centre of disc with pin joint (about which it can rotate freely), otherend of the rod is attached to a small smooth ring B, which can move freely over rod OP. At an instant rod ABmakes an angle 60° with the vertical. The velocity of ring on the vertical rod at this instant is

O

B60° A

R0

P

(A) 03 3

v2

(B) 03 v2

(C) 0v (D) 0v2

36. A planet revolves around the sun in an elliptical orbit of eccentricity e. If T is the time period of the planet,then the time spent by the planet between the ends of the minor axis and major axis close to the sun is

(A) 1 eT4 2

(B) T.e

(C) e 1 T (D)

Te

37. A container has two immiscible liquids of densities 1 and 2 (>1). A capillary tube of radius r is insertedin the liquid so that its bottom reaches upto the denser liquid. The denser liquid rises in the capillary andattains a height h from the interface of the liquids, which is equal to the column length of the lighter liquid.Assuming angle of contact to be zero, the surface tension of heavier liquid is

h 1

2

(A) 22 r gh (B) 2rgh2

(C) 2 1

r gh2 (D) 2 12 r gh


PHYSICS


38. When wave of wavelength 0.2 cm is made inciddent normally on a slit of width 0.004m, then the semi-angular width of central maximum of diffraction pattern will be-(A) 600 (B) 300 (C) 900 (D) 00

39. A string of length l is fixed at both ends. It is vibrating in its third overtone. Maximum amplitude of theparticles on the string is A. The amplitude of the particle at a distance l/3 from one end is

(A) A (B) 0 (C) 3A2

(D) A2

40. A soap bubble in vacuum has a radius of 3 cm and another soap bubble in vacuum has a radius of 4 cm. Iftwo bubbles coalesce under isothermal conditions then the radius of the new bubble is

(A) 2.3 cm (B) 4.5 cm (C) 5 cm (D) 7 cm

41. An electric field line emerges from a positive point charge +q at angle to the straight line connecting it to

a negative point charge – 2q as shown in figure. At what angle will the field line enter the charge – 2q ?

q –2q

(A) (B) 1 12sin sin

22 (C)

1 1sin sin22

(D)

1 1sin sin22 2


PHYSICS


42. A capacitor having capacitance ‘C’ is charged by a battery having e.m.f. 2V (Battery is disconnected aftercharging) . Now this charged capacitor is connected to another battery having e.m.f. V. The positive plate ofcapacitor is connected with –ve terminal of battery & vice-versa. The amount of heat produced after connectingit with battery.

(A) 4.5 CV2 (B) 1.5 CV2 (C) 4 CV2 (D) none of these

43. In the figure shown, the potential difference between points A and B is (assume all capacitors were initiallyuncharged) :

(A) 10V (B) 30V (C) 7.5V (D) none

44. An object 1 cm tall is placed in front of a mirror at a distance of 4 cm. In order to produce an upright imageof 3cm height one needs a

(A) convex mirror of radius of curvature 12 cm (B) concave mirror of radius of curvature 12 cm

(C) concave mirror of radius of curvature 4 cm (D) plane mirror of height 12 cm


PHYSICS


45. The light ray is incident at angle of 60° on a prism of angle 45°. When the light ray falls on the other surface

at 90°, the refractive index of the material of prism and the angle of deviation are given by

(A) 3, 302

(B) 15,5.1 (C) 3

, 302

(D) 3, 152

46. A plano-convex lens has a thickness of 4 cm. When placed on a horizontal table with curved surface incontact with it, the apparent depth of the bottom most point of the lens is found to be 3 cm. If the lens isinverted such that the plane face is in contact with the table, the apparent depth of the centre of plane faceis found to be 25/8 cm. The focal length of the lens is

(A) 50 cm (B) 75 cm (C) 100 cm (D) 150 cm

47. A charge q is placed at some distance along the axis of a uniformly charged disc of surface charge density

. The flux due to the charge q through the disc is . The electric force on charge q exerted by the disc is

(A) (B) 4

(C) 2

(D) 3

48. A cylindrical conductor AB of length l and area of cross-section a is connected to a battery having emf E and

negligible internal resistance. The specific conductivity of cylindrical conductor varies as 0lx

, where

0 is constant and x is distance from end A. What is the electric field just near the end B of cylinder?

(A) El

(B) 3E2l

A B

E

(C) 2E3l (D)

E2l


PHYSICS


49. A conducting disc of radius R is rotating with an angular velocity . Allowing the fact that electrons are thecurrent carries in conductor, the potential difference between the centre of the disc and edge is (mass andcharge of electron is m and e and neglect gravity)

(A) 2m RV

2e

(B) 2 2m RV

2e

(C) 2m RV

e

(D) 2 2m RV

4e

50. An electric dipole is placed along the x-axis at the origin O. A point P is at a distance of 20cm from the origin

such that OP makes an angle 3

with the x-axis. If the electric field at P makes an angle with the positive

direction of x-axis, the value of would be

(A) 3

(B) 1 3tan

3 2

(C)

23

(D) 1 3tan2

51. In the diagram shown, the charge +Q is fixed. Another charge +2q, is projected from a distance R from thefixed charge. Minimum separation between the two charges if the velocity becomes half of the projectedvelocity, at this moment is (Assume gravity to be absent)

60°

V

M,+2q+Q R

(A) 3R (B) 3

R2

(C) 1R2

(D) 4R


PHYSICS


52. A capacitor of capacitance of 2 F is charged to a potential difference of 200 V, after disconnecting from thebattery, it is connected in parallel with another uncharged capacitor. The final common potential is 20 V, thecapacitance of second capacitor is:(A) 2 F (B) 4 F (C) 18 F (D) 16 F

53. A man with normal vision uses a magnifying lens of focal length 10 cm. Choose the INCORRECT of thefollowing(A) Magnification of any value is possible(B) Maximum magnification possible is 3.5(C) Minimum magnification possible is 2.5(D) Magnification depends upon the distance of the lens from the eye

54. A galvanometer of coil resistance 1 is converted into voltmeter by using a resistance of 5 in series andsame galvanometer is converted into ammeter by using a shunt of 1. Now ammeter and voltmeter connectedin circuit as shown, find the reading of voltmeter and ammeter.

V

15 15 64.5 12

30V

(A) 3 Volt, 3 amp (B) 2 volt, 2 amp (C) 4 Volt, 3 amp (D) 3 volt, 4 amp


PHYSICS


55. A uniform sphere of mass M and radius R exerts a force F on a small mass m situated at a distance of 2Rfrom the centre O of the sphere. A spherical portion of diameter R is cut from the sphere as shown in figure.The force of attraction between the remaining part of the sphere and the mass m will be

R m

2R

O

R

(A) 7F9

(B) 2F3

(C) 4F9

(D) F3

56. There are three point objects A, B and C of mass M, m and m respectively placed on a smooth surface onan x-y plane. Among them A and C are fixed while B can move. There is a massless target T that is placedat distance r from the object B and the line joining B and T makes an angle of 300 with x-axis. Then the valueof M (in terms of m) so that the point object B can hit the target T (a >>r ) is (assuming only mutual gravitation

force of attraction between the point objects)

a

aB(m)x-axis

T

30°r

C(m)

y-axis

A(M)

(A) m2

(B) 3

m2

(C) 3m (D) m3



PHYSICS57. In the circuit shown in figure when switch S1 is closed and S2 is open, the ideal voltmeter shown a reading

18 V. When switch S2 is closed and S1 is open, the reading of the voltmeter is 24V. When S1 and S2 both areclosed, the voltmeter reading will be:

(A) 14.4 V (B) 20.6 V (C) 24.2 V (D) None of these

58. A copper sphere is suspended in a evacuated chamber maintained at 300 K. The sphere is maintained atconstant temperature of 900 K by heating electrically. A total of 300 W electric power is needed to do this.When half of the surface of the copper sphere is completely blackened, 600 W is needed to maintain thesame temperature of sphere. The emissivity of copper is

(A)14

(B) 13

(C) 12

(D) 1

59. The pressure of a monatomic gas increases linearly from 4 105 N/m2 to 8 105 N/m2 when its volumeincreases from 0.2 m3 to 0.5 m3. The work done by the gas and increase in its internal energy are given by

(A) 1.8 105J, 1.8 105J (B) 4.8 105J, 4.8 105J

(C) 1.8 105J, 4.8 105J (D) 4.8 105J, 1.8 105J

60. Unlike a laboratory sonometer, a stringed instrument is seldom plucked (i.e. position of anti node) in themiddle. Supposing a sitar string is plucked at about 1/4th of its length from the end, the most prominentharmonic would be(A) eighth (B) fourth (C) third (D) second




61. Which of the following cation is not satisfying the given reactionM+x + KI(aq.) MIx + I2(A) Cu2+ (B) Pb4+ (C) Fe3+ (D) Bi3+

62. Which ether can not be hydrolyzed by dil. H2SO4

(A) O CH2 (B) O OCH3

(C) O CH3 (D) O

63. If the radius of Al2713 nucleus is taken to be x then the radius of Te125

53 nucleus is nearly :

(A) 3/1

1353

x (B) 3x5

(C) 5x3

(D) x.5313 3/1

64. Consider the following series of reactionsM(Metal solid) + dil.HNO3 M+x (aq.) + NO(g)M+x (aq.) + Na2CrO4 yellow pptIn above reaction, metal M is(A) Ca (B) Ag (C) Pb (D) Ba




CHEMISTRY65. What are the number of diastereomers possible for D(–)-fructose ?

C=OHO H

OHHOHH

CH OH2–D(–)–Fructose

CH –OH2

(A) 4 (B) 5 (C) 6 (D) 7

66. The pressure of H2(g) required to make the potential of Hydrogen-electrode zero in pure water at 298 K, is:(A) 10–10 atm (B) 10–4 atm (C) 10–14 atm (D) 10–12 atm

67. Consider the following series of reactions

CaC2O4 CaO + Gas X + CO

Gas 'X' + NaOH (aq.) solution 'Y'Solution 'Y' + Cu(NO3)2 ppt 'Z'ppt 'Z' is(A) Green colour compound (B) White colour compound(C) Yellow colour compound (D) Brown colour compound

68. What is the major product obtained in the given reaction-

OH

+ CH –CH –Cl3 2

CH –CH –O / ethanol3 2 ?

(A) O (B) CH2 = CH2 (C)

O

(D)

O



CHEMISTRY69. For a reaction, (A B)

If the time required for 99% completion is twice the time required for 90% completion then the correct graphfor the reaction will be :

(A)

[A]

Rate(B)

[A]

Time

(C) t1/2

[A]t=0

(D) None of these

70. Fused electrolyte is used in refining of which metal(A) Aluminium (B) Copper (C) Zinc (D) Silver

71. CH3–CH=CH2

(i) Br /H O2 2

(ii) KOH (alc)(iii) H–Br

Final product is –

(A) CH –CH–CH3 2

Br

OH

(B) CH –CH–CH3 2

OH

Br

(C) CH –C–CH3 3

OH

Br

(D) CH –C–CH3 3

O


CHEMISTRY


72. CO2(g) CO(g) H2O(g)fHº (kJ mol–1) –390 –100 –240

The enthalpy for the following reaction (in kJ mol–1) isCO2(g) + H2(g) CO(g) + H2O()

(Given :vapH (H2O()) = 40 kJ mol–1)(A) 50 (B) – 50 (C) 10 (D) –60

73. Which step is involved in extraction of Pb from PbCO3(A) Froth flotation (B) Roasting (C) Self reduction (D) Electrorefining

74. Most reactive towards SN–Ar (Nucleophilic Aromatic Substitution)

(A)

BrNO2

NO2

(B)

Br

NO2

NO2

(C)

Br

NO2

(D)

Br

NO2

75. 1000 litre hard water contains 2220 mg CaCl2, 1900 mg MgCl2 and 3240 mg Ca(HCO3)2. The degree ofhardness of hard water is :(A) 2 ppm (B) 6 ppm (C) 2000 ppm (D) 6000 ppm



76. Which process is endothermic in blast furnance(A) Reduction of Fe2O3 (B) Formation of slag (C) Fusion of iron (D) Combustion of carbon

77. Number of optically active compounds obtained is -

CH3

ClH

CH2CH3

Cl /Light2

(mono chlorination)

(A) 3 (B) 4 (C) 5 (D) 6

78. Find the standard cell potential (in volt) involving the cell reactionIn2+ (aq) + Cu2+ (aq) In3+ (aq) + Cu+ (aq) at 298 K.

Given : voltzE;voltyE;voltxE oIn|In

oIn|In

oCu|Cu 232

(A) x + y – z (B) x + y – 2z (C) x + z – 2y (D) None of these

79. Which is the correct IUPAC name of co-ordination isomer of [Pt(NH3)4] [Pd(C2O4)2](A) Diamineoxlatoplatinum(II)diammineoxlatopaladate(II)(B) Diammineoxlatopaladium(II)diammineoxlatoplatinate(II)(C) Tetraammineplatinum(II)bisoxlatopoladate(II)(D) Tetraamminepaladium(II)bisoxlatoplatinate(II)


CHEMISTRY


80. Which one of the following has the same value as fH° [CO, g] ?

(A) 21fH°(CO2, g) (B)

21CH° (C(s, graphite))

(C) CH° (C(s, graphite)) – cH°(CO, g) (D) fH° (CO2, g) – fH° (C(s, diamond))

81. Which carbonyl compound doesn't release CO2 on heating ?

(A) CH –C–COOH3

O

(B)

COOH

COOH (C) CH2

COOH

COOH(D) CH –C–CH –COOH3 2

O

82. A student carried out an experiment to find the order of reactivity of five metals. They were tested with coldwater, hot water and steam and the results recorded in given table. Select correct order of metals from mostreactive to least reactive.Metal Cold water Hot water SteamV No reaction Reacts slowly Vigorous reactionW No reaction No reaction Slow reactionX Reacts slowly Vigorous reaction Not attemptedY No reaction No reaction No reactionZ Vigorous reaction Explosive Not attempted(A) V, W, Y, X, Z (B) W, X, Z, V, Y (C) Z, X, V, W, Y (D) Z, X, Y, W, V

83. Which reaction gives the product with maximum chlorine content.

(A) CCl –CHO + 23

Cl

H Product (B) 3Cl2

h(Addition Reaction)

Product

(C) 2CHCl3 Ag Powder

Product (D)

Cl2AlCl3

Product



CHEMISTRY84. A typical neutron-initiated fission of 235U yields Mo97

42 , two neutrons and an isotope of element.

What is the mass number of an isotope?(A) 138 (B) 137 (C) 136 (D) 135

85. Possible value of |x – y| for diamagnetic octahedral neutral complex Pt. xNH3.Cly(A) 3 (B) 2 (C) 1 (D) 0 (Zero)

86. Which of following compound is unreactive towards Grignard's reagent ?

(A) CH3CH2C CH (B) (C) CH – CH2 2

O(D) (CH CH ) N3 2 3

87. For which of the following process S is negative?(A) H2(g) 2H(g) (B) C(diamond) C(graphite)(C) 2SO3(g) 2SO2(g) + O2(g) (D) O2(g, 1atm) O2(g, 8 atm)



CHEMISTRY88. Which of the following statement does not support to the fact that “NH3 is stronger lewis base than PH3”

(A) Lone pair at nitrogen in NH3 molecule is more directional than lone pair at phosphorous in PH3 molecule.(B) Negative charge density at N–atom in NH3 is higher than at P-atom in PH3(C) Lone pair at P-atom in PH3 is delocalized(D) NH3 is better reducing agent than PH3

89. Given : 2.303RT

F = 0.06, log 2 = 0.3

The emf of following cell isPt, H2(g) | 1.0 M NaCl(aq) || H+ (aq, pH = 5) | H2(g), Pt 1 bar 1 bar(A) 0.12 V (B) –0.12 V (C) 0.06 V (D) –0.06 V

90. Identify the reaction which can not give 3º-Alcohol CH –CH –C–CH –CH3 2 2 3

CH3

OH

(A)

O(i) CH CH Mg Br3 2

+ –

(ii) H(B)

O(i) CH –Mg Br3

+ –

(ii) H

(C)

O (i) CH –Mg Br3+ –CH (2eq)2

(ii) HCH –C–OCH3 3 (D)

O (i) CH –Mg Br3+ –(2–eq)

(ii) HCH – C–OCH3 3CH –2














C. Marking Scheme :



CODE - ADATE : 31-07-16




















CODE - A


DATE : 28-08-16




1. Solution of the differential equation 22233 x–yyydxdyx

(A) y + x2 – y2 = cxy (B) cxx–yy 22 (C) cxyx–yy 22 (D) cxyx–yx 22

2. Let A and B be 3 × 3 symmetric matrices such that X = AB + BA and Y = AB – BA, then (XY)T is equal to[(XY)T is the transpose of matrix XY](A) XY (B) YX (C) –XY (D) – YX

3. If 2

......!4

–!2

1–cot......!7

–!5!3

––tan42

1–753

1–

then maximum value of

equals to

(A) 21– (B) 1 (C)

21

(D) 21

4. The equation of normal to the circle (x – 1)2 + (y – 2)2 = 4 which is at a maximum perpendicular distance fromthe point (–1, –1) is(A) x + 2y = 5 (B) 2x + y = 4 (C) 3x + 2y = 7 (D) 2x + 3y = 8



MATHEMATICS


5. If

5723

A

12–11–

=

401–2

, then trace of A is equal to

(A) – 25 (B) – 21 (C) – 15 (D) – 11

6. The value of

11 x

x

x 00

lim by a(1– y) dy

is equal to (where a b)

(A)

1b b–a

a1 be a

(B)

1b b–a

aba

(C)

1b b–a

abea

(D)

1a b–a

bab

7. If f(1) = 3, f (1) = 2, f (1) = 4 and let f –1(x) = g(x), then g (3) is equal to :

(A) –1 (B) –2 (C) 1–2

(D) 2

8. If A is a square matrix of order 5 and 9A–1 = 4AT then |adj(adj(adjA))| contains number of digits (log103 = 0.477,log102 = 0.301) before decimal equal to :(A) 56 (B) 57 (C) 58 (D) 59


MATHEMATICS


SECTION - IIComprehension Type

This section contains 2 groups of questions. Each group has 3 multiple choice questions based on aparagraph. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONLY ONE iscorrect.

Paragraph for Question Nos. 9 to 11Consider the following matrices

P =

2 –2 –4–1 3 41 –2 –3

, Q =

–4 –3 –31 0 14 4 3

, R =

123

and X =

xyz

9. The value of det(P + P2Q2 + P3 + P4Q4 + P5 + P6Q6 + ...... upto 100 terms) is equal to :(A) 100 (B) 150 (C) –50 (D) 0

10. The system of linear equation PX = R is(A) Consistent with unique solution (B) Inconsistent(C) Consistent with infinite solutions (D) Consistent and possess trivial solution

11. If Q–1 = Q2 –Q – I, where I is an identify matrix then equals :(A) 9 (B) 7 (C) –1 (D) –2


MATHEMATICS


Paragraph for Question Nos. 12 to 14Let y'(x) (x) – y(x) (x) + y2(x) = 0, y(1) = 1, x R, (x) and y(x) are non constant differentiable function onR with (1) = 0 and (2) = 4.

12. The value of y(2) is equal to :(A) 0 (B) 1 (C) 2 (D) 4

13. The value of 2

21 2 2

(x) 1y(x) (x)x x

y(x)

dx is equal to :

(A) 5 (B) 5 – 1

2(C) 5 – 1 (D) 5 – 2

14. Which one of the following statement is correct for function g(x) = (x)

y(x)

(A) g(x) is decreasing on R (B) Area bounded by g(x) and coordinate axes is 14

(C) g(x) has minima but no maxima (D) |g(x)| is continuous but not differentiable on R


MATHEMATICS


SECTION - IIIMultiple Correct Choice Type


15. A curve y = 2x – 3x3 is intersected by a line y = c at points A(a, c) and B(b,c), b > a, in the first quadrant. Ifthe area bounded by y-axis, the curve and the line y = c is equal to area bounded by the line y = c and thecurve (both the regions are in first quadrant), then

(A) c = 23 (B) b =

23

(C) b

3

0

(2x – 3x ) dx = bc (D) c = 49

16. Let n N, n > 11, then 1357 ........... (2n – 1) is

(A) Less than 2n–1

22n – 1e

(B) Less than 2n 1

22n 1e

(C) Greater than 2n–1

22n – 1e

(D) Greater than 2n 1

22n 1e


MATHEMATICS


17. If ABC is a triangle such that 3 sinC = 2secA – tanA and one of sides is of length 2 units, then

(A) Minimum area of triangle is 23

(B) Maximum area of triangle is 4 3

(C) Minimum area of triangle is 3

2

(D) Maximum area of triangle is 2 3

18. If (x + 1) (x + 2) (x + 3) ....... (x + 99) = A0+A1x + A2x2 + ..... + A99x99 and

99

rr 1

rA

(100)!

= 99

ii 1

1r

,where

ri < rj i < j, then the value of 99

kk 1

1r – 1

is greater than or equal to :

(where [.] denote greatest integer function)(A) 16 (B) 17 (C) 18 (D) 19


MATHEMATICS


SECTION - IVMatrix - Match Type



P Q R S

P

P

P

Q

Q

Q

R

R

R

S

S

S

A

B

C

D

P Q R ST

T

T

T

T

19. Column-I Column-II(A) Number of possible 4 digit numbers of (P) 62

the form a1a2a3a4 such that a1 > a2 a3 > a4 is

(where ai represent digits of the number)

(B) Number of divisors of N = 23 × 56 × 78 (Q) 63

of the form 4 + 2, 2 is

(C) If f : {x1,x2,x3,x4,x5} {y1,y2,y3,y4}, then (R) 120

number of possible functions 'f' in which f(xi) yi is

(D) The number of triangles that can be formed (S) 324

by joining the 3 vertices of a convex polygon of 35 diagonals is

(T) 330


MATHEMATICS


20. Column-I Column-II(A) A function y = f(x) satisfies f (x) = 6(x – 1). If its (P) 0

graph passes through the point (2,1) and at that point

the tangent to the graph is y = 3x – 5, then 2

0

f(x) dx is equal to

(B) The value of

2 3

2–2

(x – x 1) dx4 – x

is equal to (Q) 1

([.] denote greatest integer function)(C) The perpendicular distance of point whose position (R) 3

vector is (1, 3, 5) from the line

ˆ ˆ ˆ ˆ ˆ ˆr i 2j 3k (i 2 j 2k)

is equal to

(D) Let P, Q, R be invertible matrices of second (S) 27order such that A = PQ–1, B = QR–1, C = RP–1, thenthe value of det. (ABC + BCA + CAB) is equal to

(T) 9




21. A solid sphere of mass M and radius R is moving on a rough fixed surface, having co-efficient of friction asshown in figure. It will attain a minimum linear velocity after a time (v0 > 0R)

v0

0

(A) gV0

(B) gR0

(C) g)R–V( 00

(D) g7)R–V(2 00

22. A cubical block of side a is moving with velocity v on a horizontal smooth plane as shown in figure. It hits aobstacle at point O. The angular speed of the block after it hits O is

va

O

(A) a4v3

(B) a2v3

(C) a2v3

(D) Zero

23. Four bulbs B1, B2, B3 and B4 of 100 W each are connected to 220 V main as shown in the figure. The readingof an ideal ammeter will be :

B1 B2 B3220V

Ammeter

B4

(A) 0.45 A (B) 9

10 A (C) 1511

A (D) None of these



PHYSICS


24. A diatomic gas is compressed from a volume of 2m3 to a volume of 1 m3 at a constant pressure of 100 N/m2.Then it is heated at constant volume by supplying 150 J of energy. As a result, the internal energy of the gas(A) Increases by 250 J (B) Decreases by 100 J(C) Increases by 50 J (D) None of these

25. A gas molecule of mass M at the surface of the Earth has kinetic energy equivalent to 0ºC. If it were to go upstraight without colliding with any other molecules, how high it would rise ? Assume that the height attainedis much less than radius of the earth. (kB is Boltzmann constant)

(A) B564 k

3Mg (B) Mg2k273 B

(C) Mg3k546 B

(D) Mg2k819 B

26. The velocity of water in a river is 18 km/hr near the surface. If the river is 5m deep, find the shearing stressbetween the horizontal layers of water. The coefficient of viscosity of water = 10–2 poise. (Assume velocityvaries linearly with depth)(A) 10–1 N/m2 (B) 10–2 N/m2 (C) 10–3 N/m2 (D) 10–4 N/m2


PHYSICS


27. A parallel plate capacitor having a separation between the plates d, plate area A and material with dielectricconstant K has capacitance C0. Now one-third of the material is replaced by another material with dielectric

constant 2K, so that effectively there are two capacitors one with area A31

, dielectric constant 2K and

another with area A32

and dielectric constant K. If the capacitance of this new capacitor is C then 0C

C is

(A) 31

(B) 34

(C) 1 (D) 32

28. In figure shown, m1 vertically oscillates with angular frequency 1. Now the system is inverted so that m2 isat top. If oscillated vertically it oscillates with angular frequency 2. If it is kept on smooth ground as shownin figure-2, what is new angular frequency.

m2

m1

Figure-1

m1 m2

Figure-2

(A) 2

21 (B) 21 (C) 2

221 (D)

21

21


PHYSICS




Paragraph for Question Nos. 29 to 31A narrow tunnel is dug along the diameter of earth. Length of tunnel is Re/2. A thin rod of mass 'm' and length

2Re exaclly fits in the tunnel as shown in figure. Coeffieint of friction between rod and surface of tunnel is

negligible. (Me is mass of earth and Re is radius of earth).

R /2e

Re

R /2e

29. Find weight of the rod.

(A) e2e

2GM m3R (B)

e2e

3GM m5R (C)

e2e

GM m4R (D)

e2e

3GM m4R

30. Find potential energy of the road.

(A) e

e

29GM m12R

(B) e

e

29GM m24R

(C) e

e

29GM m6R

(D) None of these

31. The minimum velocity imparted to the rod, so that it escapes the gravitational field of earth is

(A) e

e

R6GM29

(B) e

e

R12GM29

(C) e

e

R3GM29

(D) e

e

RGM29


PHYSICS


Paragraph for Question Nos. 32 to 34Consider two hollow spheres of same radius R with uniform volume charge density and (– ) with centresat C1 and C2.They are merged into each other with common centreNow electric field within the common volume is zero as net charge density is zero every where. Now suppose

one sphere is very slightly shifted with respect to the other such that 1 2C C

= 0dr

. Charge density within the

common volume is still zero. But there is a charge density in the regions shown.

C1

C2

–

++

+ + + + +

–– – – – – –

–

dr =C C0 1 2++

+ +++ + + ++

++

++ ++

++

––

– – – – –– –

– –– ––

–––

If position vector of some point with respect to C1 is r , then position vector of same point with respect to C2

is r – 0dr

. By superposition principle net electric field at that point is = 0 0

0 0 0

(r dr ) drr3 3 3

. This

net electric field does not depend on r .So electric field due to such a charge distirbution is uniform within the

spherical volume. Note that 0dr

is infinitesimally small so chargefree volume after shift of spheres can be

taken to be spherical.

32. Now the charge dq enclosed in the small cylindrical volume of base area dA (as shown in the figure at anangle from line joining C1C2) can be taken to be attached to the surface as surface charge. What is thesurface charge density at the angle from line C1C2 in the above arrengement ?(A) = (dr0 cos ) (B) = (2dr0 cos ) (C) = (dr0 sec ) (D) = (2dr0 sec )

33. If a conducting sphere is placed in a uniform electric field E

, what is the electric field within the conductor byonly the charge induced on the conductor?

(A) uniform and – E

(B) non uniform (C) uniform and E

(D) Data insufficient

34. In the above question of conducting sphere in a uniform electric field E

, what is the total charge induced onthe hemisphere facing the electric field ?(A) – 6E R20 (B) – 2E R20 (C) – 3E R20 (D) – 4E R20




Multiple Correct Choice TypeThis section contains 4 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for itsanswer, out of which ONE OR MORE is/are correct.

35. Consider a conductor with a spherical cavity as shown. There is a charge + Q placed outside and a negativecharge –q inside the cavity to the left of the centre of cavity. Now choose the correct statement(s).

Q–q

(A) Force acting on –q must be towards left(B) Force acting on +Q will be towards left(C) Force on +Q will change if –q is displaced slightly from its position.(D) Force on –q will change if +Q is displaced slightly from its position.

36. Which of the following will have different time period if taken to the moon?(A) A torsional pendulum(B) A physical pendulum(C) A spring-mass system placed vertically(D) An hour-glass clock, which is essentially a vessel filled with liquid emptying through a hole in the bottom.



PHYSICS37. If you ever slapped someone or got slapped youself, you probably remember the burning sensation on your

hand or your face. Imagine you had the unfortunate occasion of being slapped by an angry person, whichcaused the temperature of the affected area of your face to rise by 1.8ºC(ouch!). Assume that the slappinghand has a mass of 1.2 kg and about 0.150 kg of the tissue on the face and the hand is affected. Alsoassume that the initial temperatue and the rate of rise of tempeature of the slapping hand and the face issame. Take the specific heat of the tissue to be 3.56 kJ/kgºC.(A) The approximate speed of hand just before impact is 40 m/s.(B) The approximate speed of hand just before impact is 30 m/s.(C) During the slapping process, heat transfer takes place between the face and the hand.(D) During the slapping process, no heat transfer takes place between the face and the hand.

38. Two dolphins swim toward each other. One of them made a sound of frequency f0. The rate of movement ofdolphins through the water is the same and equal to v. The speed of sound in water is u.(A) frequency heard by sound making dolphin is f0

(B) frequency heard by other dolphin is 0fv–uvu

(C) wavelength of sound heard by other dolphin is 0f

v–u

(D) sound approaches the other dolphin with a relative speed of u + 2v.


PHYSICS


SECTION - IVMatrix - Match Type



P Q R S

P

P

P

Q

Q

Q

R

R

R

S

S

S

A

B

C

D

P Q R ST

T

T

T

T

39. A narrow slit S transmitting light of wavelength is placed a distance d above a large plane mirror as shownin the figure. The light coming directly form the slit and that coming after the reflection interfere at a screen placed at a distance D from the slit. Assume that the mirror is 100% reflecting and d << D. Match thequantities in Column-I with their corresponding values in Column-II. (Given : D = 1meter , d = 100 )

s

d

DO

Column I Column II(A) Distance from O, where first interference maximum is formed on screen (P) 0(B) Distance from O, where closest interference minimum is formed on screen (Q) 1/4 cm(C) Fringe width of the interference pattern (R) 1/2 cm(D) Closest point to O on screen where waves interfere with a phase differene of /2 (S) 1 cm

(T) 1/8 cm


PHYSICS



(A) R R

Bubbles

merged isothermally toform a single bubble

(P) Surface energy increases

(B) R

Drops

merged isothermally toform a single bubble

R (Q) Surface energy decreases

(C)

Air Blowbubble is expanded by pushingsome air into it.

Bubble

(R) Pressure inside increases

(D)

Air bubble is given some negative charge

Bubble

(S) Pressure inside decreases

(T) Surface tension decreases




41. Which species present at cathode and in anode mud respectively, in electrorefining of impure copper containingimpurity of gold in presence of CuSO4 + H2SO4 as electrolyte(A) Cu, Au (B) Cu, Au+ (C) Au+, Cu (D) Au, Cu

42. The conductivity of a saturated solution of CaF2 at 25ºC is 6 × 10–6 S.cm–1. The conductivity of pure water is2 × 10–6 S.cm–1. If m

for Ca2+ and F– ions are 72 and 64 S.cm2.mol–1 then Ksp of CaF2 is(A) 4 × 10–10 (B) 3.2 × 10–14 (C) 9.8 × 10–14 (D) 9 × 10–10

43. Cl OH

H H

Alc. KOH (A), Product (A) is :

(A) OH H

H OH

(B) O (C) Cl H

H OH

(D)

O



CHEMISTRY


44. A appratus containing iron wool is inverted in water (X = initial level of water ).

x

ironwool

water

After three days, which situation is shown.

(A) x (B) x

(C) x (D) x

45. Select the correct increasing order of 10Dq value for chromium complexes :(1) [Cr(en)3]

3+ (2) [Cr(ox)3]3– (3) [CrF6]

3– (4) [Cr(H2O)6]3+

(A) 4 < 3 < 1 < 2 (B) 3 < 4 < 2 < 1 (C) 4 < 3 < 2 < 1 (D) 3 < 4 < 1 < 2

46. In Duma’s method for estimation of nitrogen, 0.25 g of an organic compound gives 40 mL of N2(g) collectedover water at 300K and 605 mm of Hg. If aqueous tension (vapour pressure) at 300 K is 35 mm of Hg then %of nitrogen in the compound is nearly.(A) 6.8% (B) 3.4% (C) 27.2 % (D) 13.6%


CHEMISTRY


47.

Cl

Cl

HNO3 (A) CH ONa3 (B) ; Product (B) isH SO2 4

(A)

Cl

OCH3

NO2

(B)

OCH3

Cl

NO2(C)

Cl

Cl

OCH3

(D)

OCH3

Cl

Cl

48. Cl Cl /h2 (1 mole)

Number of dichlorination product obtained by fractional distillation.(A) 3 (B) 4 (C) 5 (D) 6


CHEMISTRYSECTION - II

Comprehension TypeThis section contains 2 groups of questions. Each group has 3 multiple choice questions based on aparagraph. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONLY ONE iscorrect.

Paragraph for Question Nos. 49 to 51A chemical reaction is a process that is usually characterized by a chemical change in which the startingmaterials (reactants) are different from the products. Chemical reactions tends to involve the motion ofelectrons, leading to the formation and breaking of chemical bonds. There are several different types ofchemical reactions and more than way of classifying them.

49. A soluble metal cation forms complex with excess NH3 solution, which statement must be true for the metalcation(A) It forms soluble complex with excess KCN (B) It forms soluble complex with excess KI(C) It is soluble in excess NaOH (D) It gives ppt with K3[Fe(CN)6]

50. Which insoluble salt is soluble in dil. HCl but not in CH3COOH(A) BaSO4 (B) CaC2O4 (C) SrCrO4 (D) PbCO3

51. Two solutions are mixed in a beaker and the mass of the beaker contents is recorded at various time aftermixing. Two solution could be

Time

Mass ofbeakercontents

(A) PbCO3 (aq) + dil. HCl (aq) (B) Na2CO3 + Pb(NO3)2(C) Ba(NO3)2 + dil. H2SO4 (D) KMnO4 / H

+ + KNO2



CHEMISTRY


Paragraph for Question Nos. 52 to 54When a substituted benzene undergoes an electrophilic aromatic substitution reaction, three differentcarbocation intermediates can be formed : an ortho-substituted carbocation, a meta-substituted carbocation,and a para-substituted carbocation. The relative stabilities of the three carbocations enable us to determinethe preferred pathway of the reaction because the more stable the carbocation, the more stable the transitionstate for its formation will be, and therefore the more rapidly it will be formed.

52.

OH

CHCl + KOH3

(A) Zn-HgHCl (B)

Identify B is :

(A)

ClCH Cl2

(B)

OHCH Cl2

(C)

OHCH3

(D)

OHCH=O

53.

NH2

CHCl + KOH3 H O3 HCOOH + PPungentSmell

Identify P is :

(A)

NH2

(B)

NC

(C)

CN

(D)

CHO

54.C–NH2

O

KOBr

Identify product

(A)

H2N

(B)

NH2

(C)

NH2

(D)

H2N


CHEMISTRY




55. Which of them is/are correct statement(s) for [Cl4 Pt Cl2 Pt(en)2]Cl2(A) Can show geometrical isomerism(B) Can show co-ordination position isomerism(C) Can show optical isomerism(D) Can show ionization isomerism

56. For given three step mechanism of a catalysed complex reaction

A + B K1

K2 IAB K3 AB + I K4 P + AA

Following curve is plotted

Select correct statement(s)(A) K3 >> K4 (B) Step-3 is a second order reaction(C) Step-2 is rate determining step (D) Overall complex reaction is exothermic



CHEMISTRY57. Which of the following reaction yield cyclohexanone as major product

(A)

OHOOC

HOOC

COOH

COOH (B)

O

O

OEt H O3

(C)

O O

CH3 (i) NaOI

(ii) H(iii)

(D)

O

COOH

COOH

HOOC

HOOC

58. Given : Pt(s) | Cl2(g) | Cl–(C1) || Cl–(C2)|Cl2(g)| Pt(s) p1 atm p2 atm

Identify in which of following condition working of cell takes place :(A) C1 > C2 and P1 = P2 (B) P2 > P1 and C1 = C2

(C) C1 < C2 and P1 = P2 (D) P2 < P1 and C1 = C2



CHEMISTRYSECTION - IV



P Q R S

P

P

P

Q

Q

Q

R

R

R

S

S

S

A

B

C

D

P Q R ST

T

T

T

T

59. Match the gases with the associated conditions in the left column with their corresponding properties in theright column :

Column-I (At 273 K) Column-II

(A) N2(g) at high pressure (P) Z > 1

(B) H2 at very low pressure (p 0) (Q) Attractive force dominating

(C) CO2(g) at 1 atm (R) pV = nRT

(D) He(g) at 2 atm (S) p(V – nb) = nRT

(T) 2

2anP V nRTv


60. Column-I Column-II (Incorrect IUPAC Name of given complex) (Correction in given name)(A) [Pt(NH3) (H2O)2Cl]Cl (P) Priority of ligands

Aminechlorodiaquaplatinum(II)chloride(B) [Cr(ox)(CN)(NCS)(H2O)2]

– (Q) Oxidation state of central metal ionCynidodiaquacyanato-N-oxlatochromium(II)

(C) [Ni(dmg)2] (R) Name of ligandDi(methyl glyoxime) nickel(IV)

(D) [Co(dipy)3]3+ (S) Numeral prefix used for ligand

tri(dipyrol) cobaltate(VI) (T) Name of central metal ion


CHEMISTRY











CODE - ADATE : 28-08-16

B. Question paper format :9. The question paper consists of 3 parts (Mathematics, Physics and Chemistry). Each

part has 4 sections.


11. Section II contains 2 groups of questions. Each question has 3 questions based ona paragraph. Each question has 4 choices (A), (B), (C) and (D) for its answer, out ofwhich only one of correct.

12. Section III contains 4 multiple choice questions. Each question has 4 choices (A),(B), (C) and (D) for its answer, out of which one or more is/are correct.

13. Section IV contains 2 questions. Each questions has four statements (A, B, C and D)given in Column I and five statements (P, Q, R, S and T) in Column II. Any givenstatement in Column I can have correct matching with one or more statement(s)given in Column II. For example, if for a given question, statement B matches with thestatements given in Q and R, then for that particular question, against statement B,darken the bubbles corresponding to Q and R in the ORS.

C. Marking Scheme :

14. For each question in Section I, you will be awarded 3 marks if you darken thebubble corresponding to the correct answer and zero mark if no bubble is darkened.In case of bubbling of incorrect answer, minus one (–1) mark will be awarded.

15. For each question in Section II, you will be awarded 4 marks if you darken thebubble(s) corresponding to the correct choice(s) for the answer, and zero mark if nobubble is darkened. In all other cases, minus one (–1) mark will be awarded.

16. For each question in Section III, you will be awarded 4 marks if you darkened thebubble corresponding to the correct answer, and zero mark if no bubble is darkened.In all other cases, minus one (–1) mark will be awarded.

17. For each question in Section IV, you will be awarded 2 marks for each row inwhich you have darkened the bubble(s) corresponding to the correct answer. Thus,each question in this section carries a maximum of 8 marks. There is no negativemarking for incorrect answer(s) for this section.




















CODE - A


DATE : 28-08-16




1. The number of ways in which four distinct balls can be kept into two identical boxes so that no box remainsempty are.(A) 4 (B) 5 (C) 6 (D) 7

2. Let C be the circle x2 + y2 = 1 in the xy – plane. For each t 0, let Lt be the line passing through (0, 1) and(t, 0). Note that Lt intersects C in two points, one of which is (0, 1). Let Qt be the other point. As t varies

between 1 and 1 + 2 , the collection of points Qt sweeps out an arc on C. The angle subtended by this arc

at (0, 0) is :

(A) 8

(B) 4

(C) 2

(D) 83

3. The absolute value of 2¯x

lim

(1 + tanx)

1xtan2xtan1n)xtan1( is :

(A) 1 (B) 12

(C) 13 (D) 4

4. Let In = 2/

0

n xdxcosx ; where n is a non-negative integer..

Then n n 2

n 2 n n – 2

I I

equals.

(A) e/2 – 1 – 2

(B) e/2 – 1 (C) e/2 – 2

(D) e/2



MATHEMATICS




5. Consider a skew symmetric matrix A =

cb

ba such that a, b and c are selected from the set

S = {0, 1, 2, ............, 9}. Then which of the following is/are correct ?(A) number of possible matrices A is 10(B) number of possible invertible matrix A is 9(C) If det A is divisible by 3, then number of possible matrix A is 4(D) If b = 1 ; then det (A + I) = 2, where I be 2 × 2 identify matrix

6. The solution(s) of the differential equation 9(2 – y)2 2

dxdy

= 4 (3 – y) is /are

(A) (3 – x)2 = y2 (y + c)(B) (x + c)2 = y2 (3 – y)(C) y = 0(D) y = 3


MATHEMATICS


7. Let A and B are involutary matrix of the same order, then identity the correct statement(s).

(A) If AB = BA ; then 2

BAAB will be involutary

(B) If AB = BA ; then AB – BA will be a nilpotent matrix(C) If A and B are inverse to each other ; then A + B will be involutary matrix(D) Both A and B are also orthogonal matrix

8. If by

ax = 1 is a tangent to the curve x = 4t ; y = t

4, t R then

(A) a > 0 , b > 0 (B) a > 0, b < 0 (C) a < 0, b > 0 (D) a < 0, b < 0

9. If (4 + 15 )n = I + f ; where n is an odd natural number, I is an integer and 0 < f < 1, then

(A) (I + f) (1 – f) = 1 (B) I is an odd integer

(C) I is an even integer (D) f = 1 – (4 – 15 )n


MATHEMATICS





P Q R S

P

P

P

Q

Q

Q

R

R

R

S

S

S

A

B

C

D

P Q R ST

T

T

T

T


(A) The solution of 1 + secx = cot2 2x

is given by x = k ; (P) 2

then k is/are(B) If , are roots of equation A(x2 + m2) + Amx + Cm2x2 = 0 ; (Q) 3

then expression A(2 + 2) + A+ C22 + 3 equals to(C) If m and n are any two odd positive integers with n < m, (R) 4

then the largest positive integer which divides all the numbersof the form, m2 – n2 is :

(D) If last digit of the number 2999 is and the last digit of 35is , (S) 8then + equals to

(T) 9


MATHEMATICS


11. Let x and y be positive real numbers such that y3 + y x – x3, then

Column-I Column-II

(A) [x1/x – y1/y] (P) –1

(B) [x1/x – 1] (Q) 0

(C) [3 – (1 – x)2] (R) 1

(D) [x2 – y2 + 1] (S) 2

(T) 3

(NOTE : [.] denotes greatest integer function)


MATHEMATICS


SECTION - IVInteger Answer Type


0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

12. Let f : [0, 1] R be a continuous function such that for any x, y [0, 1]x f(y) + y f(x) 1

The maximum value of

1

0

dx)x(f can be expressed as qp

where p and q are relatively prime positive

integers. Find the value of (p + q).

13. Let 'n' be a non-negative integer and

I(n) =

0x2cos1

x)1ncos(nxcos2x)1ncos(xcos22 dx

Find the unit digit in the real number

)7(I

.



MATHEMATICS14. Find the sum of all positive integers 'n' for which

222

333

n......21)n2(........21

is also an integer.

15. Find the number of values of 'a' for which the curves y = ax2 + ax + 241

and x = ay2 + ay + 241

touch each

other.

16. The minimum value of the real constant 'a' can be expressed as qp

where p and q are relatively prime positive

integer for which f (x) 0 x R for the function f(x) = ax – 2

3

x1x

. Find (p – q)



MATHEMATICS17. Consider the system of equations

2yz + zx – 5xy = 2yz + 2xy – zx = 1yz – 2zx + 6xy = 3

Find |xyz|.

18. If A and B are square matrices of the same order such that |A| = |B| = 1 and A(adj A + adj B) = B.Find the abosute value of |A + B|.(where |M| = det M).

19. Let f(n) =

21n (where [.] denotes greatest integer function) n N

Evaluate

1nn

)n(f)n(f

222




20. ABCDEF is a closed container like a prism placed such that face ACDE is lying horizontally. A liquid ofuniform density is filled inside the container. Let F1 is the force due to liquid on the face ABC and F2 is the

force on the face ABFE. The ratio of 2

1

FF

is (assume that pressure at line FB is zero)

F B

AE

Ba

a

a

4a

C

(A) 23

(B) 32

(C) 43

(D) 341

21. Light from a monochromatic slit passes a special cylindrical plano convex lens whose plane surface is madeof two planes as shown. The radius of curvature of the curved face is 20. Find fringe width.

20cm80cm

176°

= 500 nm

S1.5

(A)

135 m (B)

180

m (C) 150

m (D) None of these



PHYSICS


22. The total length of a sonometer wire between fixed ends is 110 cm. Two bridges are placed to divide thelength of wire in ratio 6 : 3 : 2. Then tension in the wire is 400 N and the mass per unit length is 0.01 kg/m.What is the minimum common frequency with which three parts can vibrate ?(A) 1100 Hz (B) 1000 Hz (C) 166 Hz (D) 100 Hz

23. A bob is attched to a thread of length to form a conical pendulum as shown. What is the time period of theconical pendulum when tension is twice the weight.

(A) g2 (B) g

22 (C) g2

2 (D) g


PHYSICS




24. An equiconvex lens of refractive index = 1.5 and focal length f is held normally to the path of a parallel beamof light. The lens is tilted through a small angle . Then(A) the new focal length is f sec . (B) the image is displaced by f from its initial position.(C) the focal length remains unchanged. (D) the image is not displaced at all.

25. Three conentric spherical shells of radius a, 2a and 4a having positive charges Q1 and Q2 and Q3 respectivelyare placed as shown. Now, shell of radius 'a' and '4a' are earthed through switch S1 and S2. A point 'P' lies ata distance 5a from the centre of shell and a point R inside the inner most shell. Now, choose the correctoption(s) when switch S1 and S2 are closed

Ra

2a 4a

5a

S2S1

P

(A) The magnitude of electricfield at 'P' and at 'R' is equal(B) The potential of inner most shell and outermost shell must be equal(C) The magnitude of charge on shell of radius 2a remain unchanged(D) Potential must drop in moving from innermost shell to middle shell


PHYSICS


26. The steady state charge on the capacitor does not depend on

V

R1

R2

C

(A) R1 (B) R2 (C) V (D) C

27. A conducting sphere of radius R and charge Q is placed near a uniformly charged non-conducting infinitelylarge thin plate having surface charge density on front surface only. (Assume that A, B, C are just insidethe sphere)

+++++++

4R

A+Q

CB O

(A) The potential difference across points B and C on the sphere is 0

R

(B) The potential difference between points B and C is zero.(C) The electric field at O due to charge on sphere is more than electric field at C due to charge on sphere.(D) Electric field at O due to charge on sphere is same as that at B.

28. Shown in figure are two uniformly charged conducting spherical thinshells. Total electric potential energy ‘U’ of the system and heatloss ‘H’ when both shell are joined by a conducting wire will be :

(A) H = R12

kQ2(B) H =

R3kQ2 RR

+Q

3R

–Q

(C) U = R2

kQ2(D) U =

R3kQ2





P Q R S

P

P

P

Q

Q

Q

R

R

R

S

S

S

A

B

C

D

P Q R ST

T

T

T

T

29. A single lens is never free from chromatic aberration. However, two thin lenses can be placed in contact toform an achromatic double lens provided that certain conditions are satisfied. Referring to achromatism in acombination of two thin lenses placed in contact, match Column-I with Column-II

Column-I Column-II(A) A double lens consisting of two convex lenses placed (P) Achromatism is not possible.

in contact. The lenses are made of different materials.(B) A double lens consisting of a convex lens placed in (Q) Achromatism is possible but the

contact with a concave lens. The two lenses are made doublet will then not behave as aof different materials and dispersive power of the material lensof convex lens is more than other.

(C) A doublet lens consisting of a convex lens placed in (R) It is possible to obtain acontact with a concave lens. The lenses are made of convergent achromatic doublet lensdifferent materials and dispersive power of material ofconcave lens is more than the other.

(D) A double lens consisting of a convex lens placed in (S) It is possible to obtain acontact with a concave lens. The lenses are made divergent achromatic doublet lens.of same material same material.

(T) None



PHYSICS


30. Some physical quantities and their dimensions are given in Column-I. Match Column-I with Column-II. Ifdimension of mass, length, time, temperatrue and current are [M], [L], [T], [] and [A] respectively.

Column I Column II

(A)K

mg2T (P) 0

T Time periodm mass of particleg acceleration due to gravityK kinetic energy of particleIf dimension of '' is given by = [MxLyTz], then x + y + z is equal to

(B)

mK2F·h

(Q) 1

wavelength of particleh plank's constantF Forcem mass of particleK kinetic energy of particleIf dimension of '' is given by = [MxLyTz], then x + y + z is equal to

(C)2Q ( )Cm·

(R) 2

C specific heat difference in temperatureQ heat given to the systemm mass of systemIf dimension of '' is given by = [MxLyTzu]Then x + y + z + u is equal to

(D)0

e

CR

x

(S) 3

R ResistanceC Capacitance0 Permitivity of mediumxe Electric susceptibility (dimensionless)If dimension of '' is given by = [MxLyTzAu] then 2x + 2y + z + u is equal to

(T) 4


PHYSICS




0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

31. An aeroplane A is flying horizontally due east at a speed of 400 km/hr. Passengers in A, observe anotheraeroplane B moving perpendicular to its (B) length, which is 30º north of east in the same horizontal plane as

shown in the figure. If the velocity of B is 200 n km/hr, find n

vB/A

30º

B

A



PHYSICS32. Three blocks A, B and C each of mass m are arranged in pulley string system as shown in the figure. All

pulleys are massless and frictionless, while all strings are light and inextensible. Coefficient of kinetic friction, between block A and horizontal surface is equal to 0.5 and force P acts on it. The value of P/mg for whichblock C does not move, is

mC

m B

mA P

33. In the circuit shown, find the value of E/R.

E

R

R 2.25 A1.5A

30



PHYSICS34. There are six plates of equal area A and separation between the plates is d (d<<A) arranged as shown in the

figure. Find the equivalent capacitance in F between points 2 and 5. Plate No.1 and 4 are connected and

plate No. 3 and 6 are connected. (Given that 0A4 F

d

)

d 1

d

2d

dd

2

3

45

6

5

35. An ideal monoatomic gas of one mole undergoes a cycic process ADBCA as shown in figure. X and Y aretwo isothermal curves at temperatures 211ºC and 127ºC respectively. If the work done by the gas in cyclicprocess is R, then find the value of . (R is the gas constant)

P

V

YX

A

DBC



PHYSICS36. The reflecting surface of two mirrors M1 and M2 are at angle = 50º as shown in the figure. A ray of light,

parallel to M2, is incident on M1. The emerging ray intersects the incident ray at an angle = 10. (in degree)Find the value of .

M2

M1

37. Two identical capacitors with charges Q0 each are connected as shown. Initial seperation between plates isd0. Now left plate of upper capacitor and right plate of lower capacitor is moved towards left with speed V in

the direction shown. The current in the circuit then can be written as N0

0

dVQ

. Find N.

–Q0+Q0v

v

+Q0 –Q0

38. An unknown cell balances 300cm of wire in a potentiometer circuit, but the balance length reduces to 280cm when a resistance of 28 is added in parallel with the cell. A standard cell of emf 1.1 V balances 220 cmon the same potentiometer. The balance length (in cm) when 48 resistance is connected across theunknown cell is 48n cm. Find n




39. Which of the following statement concerning radial probability density (R2(r)) and radial distribution function(4r2.R2(r)) for a s-orbital of H-like species is correct ?(A) R2(r) is minimum at nucleus but 4r2.R2(r) is maximum at nucleus.(B)R2(r) is maximum at nucleus but 4r2.R2(r) is minimum at nucleus.(C) Both R2(r) and 4r2.R2(r) are maximum at nucleus.(D) Both R2(r) and 4r2.R2(r) are minimum at nucleus.

40. Dil. HNO3 does not react with.(A) Ag2CO3 (B) HI (C) PbO2 (D) HgO

41. CH –C–3

O

–C–OH

O

? CH –C–3

O

–CH –OH2

Best appropriate reagent for above conversion ?(A) (i) LiAlH4/H3O, (ii) H2CrO4(B) (i) HO–CH2–CH2–OH/H (ii) LiAlH4/H3O

(C) (i) LiAlH4/H3O (ii) HO–CH2–CH2–OH/H

(D) (i) HO–CH2–CH2–OH/H (ii) NaBH4/H3O

42. Given : Ag(s) | AgBr(s)| Br–(1.0 M) || Cl–(0.5 M) | AgCl(s) | Ag(s)The emf of following cell is 0.12 V then the ratio of Ksp(AgCl) and Ksp(AgBr) is :

[Given : 2.303 RTF

= 0.06]

(A) 50 (B) 100 (C) 150 (D) 175



CHEMISTRY




43. Correct statement(s) for extraction of copper from chalcopyrite is/are(A) Ore is concentrated by froth floatation without using depressant(B) Roasting stage occurs at lower temperature than temperature of bessemerisation stage(C) Impurity of iron is removed in the form of ferric silicate(D) Cu2O present in blister copper, is reduced to metallic copper during poling

44. Solubility product constants of two sparingly soluble salts AX and BX2 are equal. Which of the following is/arecorrect deduction?(A) Solubility of AX is greater than solubility of BX2.(B) If S1 and S2 are molar solubility of AX and BX2 then S1 = (S2)3/2

(C) If X is a conjugate base of a weak acid, addition of HNO3 will increase solubility of both AX and BX2.(D) Solubility of both AX and BX2 will increase upon dilution.

45. Correct statement(s) regarding given reaction sequence ?

32 2

4

O| |

(i)CH C HBr NaNH2 2 CCl (3 equivalent ) (ii) H

CH CH P Q R

(A) R is But-3-yn-2-ol(B) Bimolecular elimination than acid-base reaction involved during P to Q(C) Q is CH CH

(D) H–C–CH –C CH2

O

4

2

NaBHH O product is positional isomer of R


CHEMISTRY


46.Filtre

Coloured precipitate(Q)

Filtrate(R)

BaCl solution2

S

Aqueous solution of salt 'P' + K [Fe(CN) ]3 6

(ppt)

Which of the following salt(s) does/do not follow to above series of reactions(A) Fe2(SO4)3 (B) CuSO4 (C) AgNO3 (D) FeCl2

47. Correct statement(s) regarding given reaction sequence ?

3 3

2 3

O (i)CH MgBr(excess) (i)NaOIH O/Zn (ii) H O (ii)H /

P Q R

(A) 3-moles of CH3-MgBr consumed(B) compound P can give idoform test positive(C) Q formed by nucleophilic addition reaction

(D) R is O

O


CHEMISTRY





P Q R S

P

P

P

Q

Q

Q

R

R

R

S

S

S

A

B

C

D

P Q R ST

T

T

T

T


(compound) (Characteristics)

(A) Pb(NO3)2 (P) Forms complex ion with excess of NaCN solution.

(B) MgCl2.6H2O (Q) Reacts with NaOH

(C) Cr(OH)3 (R) Forms diamagnetic compound with excess of NH3 solution

(D) Ag2S (S) On heating in air metal oxide is produced

(T) Water insoluble compound dissolves in hot dil. HNO3


CHEMISTRY


49. Column-l Column-ll

(A) NH2

3CHClKOH/ (P) Carbanion is intermediate

(B) C–NH2

OH

D KOBr (Q) Carbene is intermediate

(C)

O–H

3(i)CHCl /NaOH(ii)H (R) Nitrene type T.S. is intermediate

(D) C = NOHH3C

H

H SO2 4

(S) Double bond equivalent is even in number

(T) Cyanide or isocyanide is product


CHEMISTRY




0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

50. Calculate number of Faradays of electricity required for complete electrolysis of 36 g of water if currentefficiency is 80%.

51. On adding excess of NH3 solution to which of the following metal cation(s) paramgnetic complex is formed.Fe2+(aq), Zn2+(aq), Cr3+(aq) , Mn2+(aq), Ni2+(aq), Cu2+(aq) , Sn2+(aq), Bi3+(aq), Rh3+(aq)


CHEMISTRY


52. Consider the following reaction :

3N (g)2

NN

NN

N

N(g)

Given : BE(NN) = 942 kJ mol–1 ; BE(N – N) = 170 kJ mol–1 and BE (N = N) = 420 kJ mol–1.The resonance energy of the product molecule of the given reaction is –156 kJ mol–1. If the standard molar

enthalpy of formation of N6 (cyclic) is x kJ/mol. Then calculate the value of 150x

.

53. Number of R-Mgx (grignard reagent) consumed are

O–Ph

OH C–O3

OH–C C

OH–O

(i) RMgX (excess)(ii) H O3



CHEMISTRY54. The potential of an electrode which originally contained 0.1 M –

3NO and 0.4 M H+ and which has been treated

by 80% of the cadmium necessary to reduce all the –3NO to NO is y × 10–1 V. Calculate the value of y.

–3NO (aq.) + 4H+ (aq.) + 3e– NO (g) + 2H2O()

[Given : E0 = 0.96 V ; log 2 = 0.3 ; PNO(g) = 8 × 10–4 bar ; 2.303 RTF

= 0.06]

55. 20 mole of an ideal monoatomic gas is subjected to following cyclic process.

A C

B

V

PT = 200KA

If 12 kcal heat is absorbed in path AB and 10 kcal heat is released in path CA, then calculate magnitude ofwork done (kcal) in adiabatic process BC.


CHEMISTRY


56. If molar conductivity of 0.1 M HX(aq.) solution is 3.9 –1 cm2 mol–1, then calculate pH of 0.1 M HX(aq.)solution.

[Given : M NaX = 90 –1cm2 mol–1 ; M HCl

= 425 –1cm2 mol–1 ; M NaCl = 125 –1cm2 mol–1]

57. x = number of optically pure aldehyde or ketone having molecular formula of C5H10O give chiral alcohol butnot racemic mixture with NaBH4/CH3–OH. (Consider enantiomer separately).









CODE - A




11. Section II contains 5 multiple choice questions. Each question has 4 choices (A),(B), (C) and (D) for its answer, out of which one or more is/are correct.

12. Section III contains 2 questions. Each question has four statements (A, B, C and D)given in Column I and five statements (P, Q, R, S and T) in Column II. Any givenstatement in Column I can have correct matching with one or more statement(s)given in Column II. For example, if for a given question, statement B matches with thestatements given in Q and R, then for that particular question, against statement B,darken the bubbles corresponding to Q and R in the ORS.

13. Section IV contains 8 questions. The answer to each of the questions is a single-digit integer, ranging from 0 to 9. The answer will have to be appropriately bubbled inthe ORS as per the instructions given at the beginning of the section.

C. Marking Scheme :

14. For each question in Section I, you will be awarded 3 marks if you darken thebubble corresponding to the correct answer and zero mark if no bubble is darkened.In case of bubbling of incorrect answer, minus one (–1) mark will be awarded.

15. For each question in Section II, you will be awarded 4 marks if you darken thebubble(s) corresponding to the correct choice(s) for the answer, and zero mark if nobubble is darkened. In all other cases, minus one (–1) mark will be awarded.

16. For each question in Section III, you will be awarded 2 marks for each row inwhich you have darkened the bubble(s) corresponding to the correct answer. Thus,each question in this section carries a maximum of 8 marks. There is no negativemarking for incorrect answer(s) for this section.

17. For each question in Section IV, you will be awarded 4 marks if you darken thebubble corresponding to the correct answer, and zero mark if no bubble is darkened.In all other cases, minus one (–1) mark will be awarded.

DATE : 28-08-16




















CODE - A


DATE : 25-09-16




1. If f(x) is continuous and increasing function such that domain of g(x) f(x) x is R and 1h(x)

1 x

, then

the domain of function (x) f(f(f(x))) h(h(h(x))) is

(A) R (B) R – {0, 1} (C) R – (0, 1) (D) None of these

2. Let f(x), g(x) and h(x) are continuous and positive functions such that

f(x) g(x) h(x) f(x)g(x) g(x)h(x) f(x)h(x) then f(x) + g(x) – 2h(x) =

(A) 0 (B) 1 (C) – 1 (D) 2

3. Let f1(x), f2(x) be twice differentiable functions where f(x) = f1(x) + f2(x) and g(x) = f1(x) – f2(x) x R, f1(0)=2

and f2(0) = 1. If f1(x) = f2(x) and f2(x) = f1(x) x R, then the number of solution(s) of the equation 5

2 9xf(x)g(x)

is equal to :(A) 0 (B) 1 (C) 2 (D) More than 2

4. If A1 = [a1], 6 7 8

2 32 3 9 10 11

4 512 13 14

a a aa a

A , A a a aa a

a a a

........An where ar = [log2r] (where [] denotes greatest integer

function). Then Tr(A10) is equal to (where Tr(A) denotes trace of matrix A)(A) 800 (B) 80 (C) 160 (D) 792




MATHEMATICS

5. If 21 /4 tan

1 2x 2 30 0

dx e sinI and I d

e (1 x) (2 tan )cos

, then 1

2

II is equal to

(A) 1e

(B) 2e

(C) 2e (D) 1

2e

6. Let r (a b)sinx (b c)cosy 2(c a)

where a, b, c

are three non-coplanar vectors, if r is perpendicular

to a b c

, then minimum value of x2 + y2 is

(A) 2

4

(B) 2 (C) 25

4

(D) None of these

7. OABC is a tetrahedron, the position vectors of A, B and C are ˆ ˆ ˆ ˆ î, i j, j k respectively. 'O' is origin, then

height of tetrahedron (taking plane ABC as base) is

(A) 12

(B) 12

(C) 1

2 2(D) None of these

8. Total no. of point(s) of extrema of the function f(x) = 5x2/5 – x2 is/are :(A) 0 (B) 1 (C) 2 (D) More than 2



MATHEMATICS

9. The set of all possible values of parameter 'a' such that the equation 22 2

2 2

x x(a 1) 3a 4a 0x 1 1 x

has a real solution is

(A) 1, 02

(B) (– 1, 1) (C)

1 1,2 2

(D) None of these

10. A line with direction ratios <2, 1, 2> intersects the lines ˆ ˆ ˆ ˆr j ( i j k)

and ˆ ˆ ˆ ˆr i (2i j k)

at AA

and B, then length of AB is

(A) 3 (B) 3 (C) 16 (D) 28

11. Let A is a square matrix such that 4 0 0

adj(adjA)A(adj A) 0 4 0 then

adjA0 0 4

(A) 256 (B) 64 (C) 32 (D) 16

12. Let f(x) = 1

nne

tan (tanx)lim1 (log x)

, such that

x 2 x 3x

2

lim f(x), lim f(x) and lim f(x)

, then | + – | =

(A) 22

(B) 22

(C) 0 (D) 3 22



MATHEMATICS

13. If are in A.P. and 2

0

f(x)dx = –2 where f(x) =

x x x –x x x –1x x x –

then the common difference of

the A.P. is :

(A) 1 (B) –1 (C) 12

(D) 1–2

14. Which of the following is NOT true.(A) For each n × n matrix A, AT.A is symmetric matrix.(B) If A is skew symmetric matrix then A.A is symmetric matrix.(C) For real x, y given X = [x y] ; A = [aij]2×2 then X.AT.A.XT can not be positive.

(D) Given A = –2 –91 4

then AAn = 1– 3n –9n

n 1 3n

where n N

15. If y = xsinx + cosx – 12

x2, – x2 2 then minimum value of y = f(x) is :

(A) 0 (B) –1 (C) 1 (D) 2

–2 8



MATHEMATICS16. If ABCD is a cyclic quadrilateral such that 12 tanA – 5 = 0 and 5 cosB + 3 = 0, then the quadratic equation

whose roots are cosC and tanD is :(A) 39x2 – 16x – 48 = 0 (B) 39x2 + 88x + 48 = 0(C) 39x2 – 88x + 48 = 0 (D) none of these

17. The fundamental period of the function, f(x) = sin2x + cos4x is

(A) 2

(B) (C) 2 (D) none of these

18.

12n

2

2n

x(sin x) dx2

is equal to (where n N and {•} represent fraction part function)

(A) n

(B) n 1

(C) 2

2n 1

(D) 2

4n 12

19. a, b, c

are unit vectors such that a b 3c 14

. Angle between vectors a

and b

is , b

and c

is , a

and c

is . If 2,

6 3

then maximum value of cos + 3 cos is

(A) 2 (B) 2 2 (C) 3 (D) 4



MATHEMATICS

20. If 1 9f(n 1) f(n)2 f(n)

n N and f(1) = 2, then nlim f(n)

is equal to :

(A) 2 (B) 12

(C) 3 (D) –3

21. If the straight lines x + y – 2 = 0, 2x – y + 1 = 0 and ax + by – c = 0 are concurrent, then the family of lines2ax + 3by + c = 0 (a, b, c are non-zero) is concurrent at :

(A) (2, 3) (B) 1 1,2 3

(C) 1 5,6 9

(D) 2 7,3 5

22. The solution of differential equation dyxcosx y(x sinx cos x) 1dx

is

(A) xy secx = tanx + c (B) xy tanx = secx + c(C) y secx = x tanx + c (D) y tanx = x secx + c

23. From the point (4, – 4) tangents are drawn to the circle x2 + y2 – 6x + 2y + 5 = 0. The length of chord joiningthe points of contact is :

(A) 10 (B) 10 (C) 20 (D) 52


MATHEMATICS


24. are roots of the equation, x3 + ax2 + bx + c = 0, (a 0) and if the system of equationsx + y + z = 0, x + y + z = 0 and x + y + z = 0 has non-trivial solutions, then a2 is equal to(A) 2b (B) 3b (C) 2(b + c) (D) 3c

25. In how many ways 10 identical balls can be placed in 3 distinct boxes, if no box remains empty ?(A) 36 (B) 72 (C) 54 (D) 18

26. The number of solutions of equation e2x = 9x2 is :(A) 0 (B) 1 (C) 2 (D) 3

27. Let f and g be two real valued functions such that f(2 – x) = 2 – f(x) and f(x) – g(x) = 1 x R, then(A) f(x) is symmetrical about the line x = 1 (B) g(x) is symmetrical about the line x = 1(C) f(x) is symmetrical about the point (1, 0) (D) g(x) is symmetrical about the point (1, 0)



MATHEMATICS

28. If d f(x) f '(x)dx

, then 4

xf '(x) 2f(x) dxx f(x)

is equal to :

(A) x2 f(x) + c (B) | x | f(x) + c (C) | x | f(x) c (D) 2 f(x)

c| x |

29. If coefficient of x7 in 11

2 1pxqx

is equal to coefficient of 7

1x

in 11

2

1pxqx

(where p, q > 0), then the least

value of p + q is :(A) 1 (B) 2 (C) 3 (D) 4

30. If x = 2 cost – cos2t and y = 2 sint – sin2t, then the value of 2

2

d ydx

at t2

is :

(A) 32

(B) 32

(C) 52

(D) 52




31. An aeroplane is rising vertically with acceleration f. Two stones are dropped from it at an interval of time t. Thedistance between them at time t after the second stone is dropped will be

(A) 1 (g f)tt2

(B) 1 (g f)(t 2t )t2

(C) 21 (g f )(t t )2

(D) 21 (g f )(t t )2

32. A direct current flows in a solenoid of length L and radius R, (L > > R), producing a magnetic field ofmagnitude B0 inside the solenoid.

B0

R

P

Which of the following diagrams best discribes the magnetic field lines in the vicinity of P at the end of thecoil.

(A) (B)

(C) (D)



PHYSICS


33. A particle is hanging from a string of length = 10 m. It is imparted a horizontal velocity of 20 m/s at thebottom. The velocity of the particle at its highest point is

(A) 203 m/s (B)

20 23 3

m/s (C) 203

m/s (D) 2203

m/s

34. A long, thin carpet is laid on a floor. One end of the carpet is bent back and then pulled backwards withconstant unit velocity, just above the part of the carpet which is still at rest on the floor. The speed of centreof mass of the moving part is

=1m/s

(A) 1 m/s (B) 34

m/s (C) 12

m/s (D) 14

m/s

35. In Young's double slit experiment the slits are 0.5 mm apart and the interference is observed on a screen ata distance of 100 cm from the slit. It is found that the 9th bright fringe is at a distance of 7.5 mm from thesecond dark fringe from the centre of the fringe pattern. The wavelength of the light used is

(A) Å7

2500(B) 2500 Å (C) 5000 Å (D) Å

75000

36. An artificial satellite of mass m is moving in a circular orbit at a height equal to the radius R of the earth.Suddenly due to internal explosion the satellite breaks into two parts of equal masses. One part of thesatellite stops just after the explosion. The increase in the mechanical energy of the system (satellite +earth) due to explosion will be(Given: acceleration due to gravity on the surface of earth is g)

(A) mgR (B) mgR

2(C)

mgR4

(D)3mgR

4


PHYSICS


37. A container has two immiscible liquids of densities 1 and 2 (>1). A capillary tube of radius r is inserted inthe liquid so that its bottom reaches upto the denser liquid. The denser liquid rises in the capillary and attainsa height h from the interface of the liquids, which is equal to the column length of the lighter liquid. Assumingangle of contact to be zero, the surface tension of heavier liquid is

(A) 2r2gh (B) 2rgh2

B

1h

2

(C) 2 1r gh2

(D) 2r(2 – 1)gh

38. A solid sphere of radius R made of a material of Bulk modulus K is surrounded by a liquid in a cylindricalcontainer. A light piston of area A floats on the surface of the liquid. When a mass m is placed on the pistonto compress the liquid, the fractional change in the radius of the sphere will be

(A) mgAK

(B) 3mgAK

(C)mg3AK (D)

mg2AK

39. In the given figure, string, spring and pulleys are massless. Block A, performing SHM of amplitude

1 meter and time period 2/ sec. If block B remains at rest, then minimum value of co-efficient of friction

between block B and surface will be (g = 10 m/s2)

m A

3mB

(A) 12

(B) 1315 (C)

23 (D)

45


PHYSICS


40. A closed organ pipe of length 99.4 cm is vibrating in its first overtone and in always resonance with a tuningfork having frequency f = (300 – 2t) Hz, where t is time in second. The rate by which radius of organ pipechanges when its radius is 1 cm, is (speed of sound in organ pipe = 320 m/s)

(A) 1

72 m/s (B)

136 m/s (C)

118 m/s (D)

19 m/s

41. Figure shows a parabolic graph between T and 1V

(T = temperature, V = volume) for a mixture of a gases

undergoing an adiabatic process. The ratio of rms velocity of molecules and speed of sound in the mixture ofgases at the same temperature is

(A) 32

(B) 2

1/V4/V01/V0

T0

2T0

(C) 23

(D) 3

42. Four metallic plates, each with surface area of one side A, are placed at a distance d from each other. Theplates are connected as shown in figure. Then the capacitance of the system between P and Q is:

(A) 03 Ad

(B) 02 Ad 1

2

34

P(+)

Q(–)(C) 02 A3d

(D) 03 A2d


PHYSICS


43. A capacitor of capacitance C1 is charged to V0 volt. The energy stored in it is U0. It is connected in parallelto another uncharged capacitor of capacitance C2. The energy loss in the process is

(A) 1 2 0

1 2

C C U2 C C (B)

21 2

01 2

C CU

C C

(C)1 0

1 2

C UC C (D)

2 0

1 2

C UC C

44. A point charge is placed at a distance r from center of a conducting neutral sphere of radius R (rR).The potential at any point P inside the sphere at a distance r1 from point charge due to induced charge of the

sphere is given by [k = 0

14 ]

R

P

C r

r1

q

(A) kq/r1 (B) kq/r (C) kq/r – kq/r1 (D) –kq/R

45. Find the equivalent resistance across AB

22

2

2

2

A

B

(A) 1 (B) 2 (C) 3 (D) 4


PHYSICS


46. A resistance of 4 and a wire of length 5 metres and resistance 5 are joined in series and connected to acell of e.m.f. 10V and internal resistance 1. A parallel combination of two identical cells is balanced across300 cm of the wire. The e.m.f. of each cell is

EE

5m5

4

G

10V,1

(A) 1.5 V (B) 3.0 V (C) 0.67 V (D) 1.33 V

47. A photographer changes the aperture of his camera so that the new diameter of the aperture is twicethe initial one, the ratio of new exposure time to the initial one to achieve same brightness is-(A) 1: 2 (B) 2 : 1 (C) 1 : 4 (D) 4 : 1

48. A particle charge q and mass m is projected with a velocity v0 towards a circular region having uniformmagnetic field B perpendicular and into the plane of paper from point P as shown in the figure. R is the radiusand O is the centre of the circular region. If the line OP makes an angle with the direction of v0 then thevalue of v0 so that particle passes through O is

Magnetic field

O

Pv0q,m

(A) qBR

msin (B) qBR

2msin (C) 2qBRmsin (D)

3qBR2msin


PHYSICS


49. Calculate the magnetic moment associated with the loop carrying current 0I as shown in the figure is

(A) 20

3 3 I a2

(B) 20

2 2 I a3

y

x

az

(C) 20

2 I a5 (D) 2

03 I a

2

50. Two infinite wires (fixed) carrying current I0 and a square loop with side 'a' also carrying the same current isplaced in space as shown in the figure.

aa

aX

O

I0

I0

R

Y

A

BC/4

D

(A) the square frame starts moving parallel to line OX towards line OY.(B) the square frame starts moving parallel to line OY towards line OX(C) the square frame starts moving along line OR away from point O(D) the square frame starts moving along line OR towards point O.

51. The lens in an overhead projector forms an image P' of a point P on an overhead transparency. If the screenis moved closer to the projector to keep the image on the screen in focus, the lens must be

(A) moved up (B) moved towards left (C) moved down (D) moved towards right


PHYSICS


52. Conducting circular loop of radius r is placed in x-y plane in gravity free space as shown in the figure, massof the loop is m and centre of the loop is at the origin. At t = 0, a current I starts flowing through the loop and

a magnetic field 0ˆ ˆB B i j

is switched on in the region (where B0 is a constant). The angular acceleration

of the loop due to the torque of magnetic field is

(A) 02 B im

(B) 02 2 B im

xir

y

(C) 0B im

(D) 0B i2m

53. A rod of length l, negligible resistance and mass m slides on two horizontal frictionless rails of negligibleresistance by hanging a block of mass m1 by the help of insulating massless string passing through fixedmassless pulley (as shown). If a constant magnetic field B acts vertically upwards perpendicular to the planeof the figure, the terminal velocity of hanging mass is

(A) 12 2

m gRB l upward (B) 1

2 2

m gRB l downward

m1

R B

(C) 12 2

m gR2B l downward (D) 1

2

m gRB l downward

54. In a uniform magnetic field of induction B, a wire in the form of semicircle of radius r rotates about thediameter of the circle with angular frequency . If the total resistance of the circuit is R, the mean powergenerated per period of rotation is

(A) RrB

2

2(B)

RrB2

)( 22

R

B

(C) RrB

2)( 2

(D) R

rB8

)( 22



PHYSICS55. A uniform electric field E is present horizontally along the paper throughout region but uniform magnetic field

B0 is present horizontally (perpendicular to plane of paper in inward direction) right to the vertical line AB asshown. A charge particle having charge q and mass m is projected vertically upward and crosses the line ABafter time t0. Find the speed of projection if particle moves after t0 with constant velocity.(given qE = mg)

(A) gt0(B) 2gt0

(C) 0gt2

EB0

A

q,m

B

g

(D) particle can’t move with constant velocity after crossing AB

56. A short wire AB carrying I1 current lies in the plane of long wire which carry I current upward. If wire AB isreleased from horizontal position and aA and aB are magnitude of acceleration of points A and B respectively,then select the correct alternative. (The space is gravity free)

I1A BI

(A) aA aB (B) aA aB (C) aA = aB 0 (D) aA = aB = 0

57. A particle of charge q, mass m starts moving from origin under the action of an electric field 0Ê E i

and

magnetic field 0ˆB B k

. Its velocity at (x, 0, 0) is ˆ ˆ6i 8 j . The value of x is

(A)0

25mqE (B)

0

100mqB (C)

0

50mqE (D)

0

14mqE


58. An uniform ring of radius R, is fitted with a massless rod AB along its diameter. An ideal horizontal string(whose one end is attached with the rod at a height r) passes over a smooth pulley and other end of the stringis attached with a block of mass double the mass of ring as shown. The co-efficient of friction between thering and the surface is . When the system is released from rest, the ring moves such that rod AB remainsvertical. The value of r is

(A) 3R 12(1 )

(B) R 12(1 )

2mB

rR

A

(C) 3R 2

2(1 )

(D)

3R 1(1 )

59. The radius of gyration of a uniform disc about a line perpendicular to the disc equals its radius r. The distanceof the line from the centre is

(A) r2

(B) r2

(C) r (D) r 2

60. A bullet of mass m moving with velocity v0 hits a wooden block A of mass M placed on a smooth horizontalsurface. The length of the block is l. The bullet experiences a constant resistive force F inside the block.The minimum value of v0 such that it is able to come out of the block is :

(A) 2

F mMl

(B) 2F (M m)

Mml

A

mv0

l

M

(C) 2

2F mM

l(D)

F (M m)lMm


PHYSICS




61. The number of dichloro derivatives of naphthalene are :(A) 10 (B) 14 (C) 6 (D) 5

62. Fe2+ (aq.) and Fe3+ (aq.) ions can be separated by :(A) NH4Cl(s) + NH4OH soln. (B) H2S + dil.HCl(C) dil.HCl (D) NH4OH soln. + H2S

63. A mixture of two immiscible liquids chlorobenzene and water boils at 90ºC and an external pressure of 720torr. If vapour pressure of pure water at 90ºC is 576 torr then the mole % of chlorobenzene in the distillate willbe :(A) 80% (B) 40% (C) 20% (D) 60%

64. Compare the rate of nitration of the following compounds.

T

T

T

T

T

T

(x)

D HD H

D HD H

D H

D H

(y) (z)

(A) x > y > z (B) z > y > x (C) x = y = z (D) y > x > z




CHEMISTRY65. Oxygen gas is produced by which of the following combination of reactants :

(A) PbO2 + hot conc.HCl (B) XeF4 + H2O(C) CaOCl2 + H2S (D) NaCl + NaClO3 + conc.H2SO4

66. The relative lowering in vapour pressure for a solution containg 1 mole CaCl2 in 180 grams H2O will be :

(A) 111

(B) 113

(C) 131

(D) 133

67. Fehling’s solution is :(A) Acidified CuSO4 solution.(B) Ammoniacal cuprous chloride solution.(C) Copper sulphate and Rochelle salt + NaOH.(D) Ammoniacal silver nitrate.

68. What part of an edge in bcc unit-cell is covered by atoms?

(A) 34

(B) 23

(C) 32

(D) 3



CHEMISTRY69. Which of the following compound, when reacts with conc. H2SO4 then at least two properties of conc. H2SO4

are used in the reaction :(A) Na2B4O7 (B) FeS (C) CaF2 (D) Ca3(PO4)2

70. Which reagent can be used to distinguish between formaldehyde and acetaldehyde ?(A) NaOH/I2 (B) Tollen’s reagent (C) Fehling’s test (D) Zn-Hg/HCl

71. Select incorrect order of solubility in water(A) PbS > ZnS > CaS (B) Mg(OH)2 > Al(OH)3(C) CrCl3 > PbCl2 > AgCl (D) BaC2O4 > CaC2O4

72. The electrolysis of 250 mL of a NaCl solution was carried out for a period of 20 minutes with a current of 2.0A. The resulting solution was titrated with 0.62 M HCl solution. The volume of HCl solution required toachieve equivalence point, is :(A) 20 mL (B) 30 mL (C) 40 mL (D) 60 mL


CHEMISTRY


73. If formaldehyde and KOH are treated together, we get :(A) Ethanol (B) Methanol (C) Ethanol (D) Acetylene

74. Phosphine gas is not prepared by(A) Heating of NaH2PO2 (B) Hydrolysis of Ca3P2(C) Warming white phosphorus with NaOH (D) Heating of Na2HPO4

75. What is two dimensional co-ordination number of a atom in square closed packed layer?(A) 6 (B) 4 (C) 8 (D) 12

76. Which of the following will give a ketone with grignard reagent ?(A) HCHO (B) EtOH (C) CH3CN (D) CH3I



77. Which of the following compound can undergo partial as well as complete hydrolysis :(A) SiCl4 (B) IF7 (C) BiCl3 (D) H3PO5

78. The activation energy for the reaction2HI(g) H2(g) + I2(g)

is 230.3 kJ/mol at 500 K. Calculate the fraction of molecules of reactants having energy equal to or greaterthan activation energy? (R = 8 J/mol).(A) 0.1 × 10–25 (B) 25 (C) 1 × 1025 (D) 1 × 10–25

79. The reagent of choice for the selective reduction of ketone in the presence of an ester is :(A) LiAlH4 (B) H2/Pd-C (C) DIBAL-H (D) NaBH4

80. Incorrect statement related to hydrolysis of XeF6 :(A) It is non redox hydrolysis reaction(B) One of the hydrolysed products can react with silica(C) XeOF4 and XeO2F2 can be isolated on partial hydrolysis(D) XeF6 can be stored safely in moist glass vessels


CHEMISTRY


81. A mixture containing equimolar amounts of CaO and Al2O3 requires 0.5 of 4.0 M HCl to react with itcompletely as following,

CaO(s) + HCl(aq.) CaCl2(aq) + H2O(l)Al2O3(s) + HCl(aq) AlCl3(aq) + H2O(l)

Then moles of CaO in the original mixture are :-(A) 0.25 (B) 0.50 (C) 0.60 (D) 0.80

82.

OH

CH3

CHCl + NaOH3

Major product of above reaction is

(A)

OH

CH3

CHO

(B)

OH

CH3

COOH

(C)

OH

COOH

(D)

OH

CH3

CHO

83. Two flask A and B of equal volumes maintained at temperautre 300 K and 600 K contain equal mass of H2

and CH4 respectively. Then the ratio of total translational kinetic energy of gas in flask A to that in flask B is(A) 1 (B) 2 (C) 4 (D) 0.25



CHEMISTRY84. For given reaction : Zn + HNO3 (very dil.) P + Q + H2O

Which of the following product can be obtained on thermal decomposition of both compounds 'P' and 'Q'.(A) NO2 (B) N2O (C) O2 (D) NH3

85. Among the given compounds, the most susceptible to nucleophilic attack at the carbonyl group is :(A) MeCOCl (B) MeCHO (C) MeCOOMe (D) MeCOOCOMe

86. In order to prepare a buffer of pH 8.26, the amount of (NH4)2SO4 required to be mixed with 1 litre of 0.1 M NH3

(pKb = 4.74) is :(A) 1 mole (B) 10 mol (C) 0.5 mol (D) 5 mol

87. Which of the following cation is not precipitated in the form of sulphide by H2S gas in the presence ofNH4OH, from its solution.(A) Bi3+(aq) (B) Cr3+(aq) (C) Fe2+(aq) (D) Zn2+(aq)



CHEMISTRY88. Out of butane, butan-1-ol and butanal the decreasing order of boiling point is :

(A) butane > butan-1-ol > butanal. (B) butan-1-ol > butane > butanal.(C) butan-1-ol > butanal > butane. (D) butanal > butan-1-ol > butane.

89. A water soluble salt was treated with excess of ammonia solution and coloured solution was appeared.However, when the given salt was treated with KI solution then white precipitate was obtained.Then which of the following salt follows above properties.(A) Fe2(SO4)3 (B) CuSO4 (C) Cu(OH)2.CuCO3 (D) ZnSO4

90. 90 g water at 0ºC is frozen at constant pressure. If enthalpy of fusion of ice is 5.46 kJ/mol, the entropychange in the process is :(A) 1800 J/K (B) – 100 J/K (C) 10 J/K (D) – 20 J/K












C. Marking Scheme :



CODE - ADATE : 25-09-16




















CODE - A


DATE : 09-10-16




1. Let z = )2/i(–)2/3( . Then the smallest positive integer n suchthat (z95 + i67)94 = zn is

(A) 12 (B) 10 (C) 9 (D) 8

2. If b,a

and c

are non zero vectors then the value of the scalar b)ab(.a)ba(

equals

(A) 2|ba|)b.a(–

(B) 22 |ba|a

(C) 22 |ba||b|

(D) 2(a.b) | a b |

3. If Z is a non real complex number then the minimum value of 5

5

))Z(Im()ZIm(

, is

(A) – 1 (B) – 2 (C) – 4 (D) – 5

4. Let , , be the roots of the equation x3 – 5x2 + 2x + 1 = 0. If a (2 5 ) i ( 3 ) j (3 2 ) k ;

b (2 5 ) i ( 3 ) j (3 2 ) k and c

= (2 + 5) i + ( + 3) j + (3 + 2) k then a bc

equals:

(A) 5 (B) – 3 (C) 1 (D) 0



MATHEMATICS


5. 1

1 2 2 2

0

cos (x x ) (1 x ) (2x x ) dx equals

(A) 0 (B) 1 (C) –1 (D) 2

6. The greatest term in the expansion of (1 + 3x)54 when 1x3

, is

(A) 28th (B) 25th (C) 26th (D) 24th

7. If 1 2 1

A 1 1 22 1 1

, then det (adj (adj A)), is

(A) 144 (B) 143 (C) 142 (D) 14

8. Minimum distance between the parabolas y2 – 4x – 8y + 40 = 0 and x2 – 8x – 4y + 40 = 0, is

(A) 0 (B) 3 (C) 2 2 (D) 2


MATHEMATICS



This section contains 2 paragraphs. Based upon the first paragraph, 2 multiple choice questions and basedupon the second paragraph 3 multiple choice questions have to be answered. Each of these questions hasfour choices (A), (B), (C) and (D), out of which ONLY ONE is correct.


| a | | b | | c | | a b | 1

. If c.a

= 0 and a

= 2j

2i and a, b and c

are linearly dependent.

9. If maximum and minimum value of b.c

is M and m respectively, then 4(M2 + m2) equals

(A) 1 (B) 5 (C) 3 (D) 6

10. If for some vector c

, | b c | | a c |

and krjqipc then 16(p4 + q4 + r4) equals

(A) 8 (B) 21 (C) 321

(D) 4


MATHEMATICS


Paragraph for Question Nos. 11 to 13A plane is determined by three points A(0, 0, 1) ; B(2, 0, 0) and C(0, 3, 0) and a line L whose vector

equation is )kj2–i2(ki38r

. The line L intersects the plane at P..

11. Distance of the point P from the origin is

(A) 2103 (B)

3102 (C) 10 (D) 102

12. A unit vector along the line of intersection of the plane and the plane 2x + y – 2z = 5, is

(A) 175kj18–i10

(B) 175kj18i10

(C) 155k–j18–i10

(D)

155

k–j18i10

13. Acute angle between the plane and the given line L, is

(A) sin–1

218

(B) cos–1

218

(C) tan–1

198

(D) None of these


MATHEMATICS




14. If 1

2

z z 3z z

where z1 and z2 are fixed complex numbers and z is variable complex number then z lies on

(A) circle with z1 as its interior point (B) circle with z1 as its exterior point(C) circle with z2 as its interior point (D) circle with z2 as its exterior point

15. If the planes ax + 3y + 5z = 2; x – y + 2z = 5 and 2x – 3y + z = 1 meet at exactly one point than the valueof 'a' may be

(A) – 12

(B) – 45 (C)

45 (D)

37

16. Let f(x) = (2x2 + 2x + 3) + 2 2

1(x x 1) than the value(s) f(x) CAN NOT take is/are.

(A) 1 (B) 2 (C) 4 (D) 5


MATHEMATICS


17. In the adjoining figure

z4 z3

z1 z21

2/3

If z3 = z1 + z2 then (where , are complex numbers).

(A) 2||||

(B) amp() + amp() = 6

(C) Area of triangle formed by origin with and is 23

(D) Circum radius of triangle formed by origin with and = 13

18. Let f(x) is a function, such that )y(f)x(f

yxf

x, y R ; y 0, f(y) 0 and slope of tangent to y = f(x) at

x = 1 is 2. If a tangent to curve : g(x) = 1 + f(x) at point (, ) makes a trapezium of greatest area with axesand line x = 1, then

(A) 4 – 2 = 4 (B) 4( + ) = 7 (C) 23

2

(D) 2

3


MATHEMATICS



This section contains 10 questions. The answer to each of the questions is a single-digit integer, rangingfrom 0 to 9. The appropriate bubbles below the respective question numbers in the ORS have to be darkened.For example, if the correct answers to question numbers X, Y, Z and W (say) are 6, 0, 9 and 2, respectively,then the correct darkening of bubbles will look like the following :In all cases round answer to nearest integer value (if required)

0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

19. If z is a complex number and 1–i , then the minimum possible value of |z|2 + |z – 3|2 + |z – 6i|2 is .

Find 6

.

20. Line is a tangent to a unit circle S at a point P. Point A and the circle S are on the same side of , and thedistance from A to is 3. Two tangents from point A intersect line at the point B and C respectively.Find the value of (PB)(PC).


MATHEMATICS


21. Consider the lines L1 :x 7 y 5 z 3

3 2 1

and L2 : x 1 y 1 z 1

2 4 3

. If a line L whose direction ratios

are 2, 2 and 1 intersect the lines L1 and L2 at A and B, find the distance AB.

22. Suppose in tetrahedron ABCD, AB = 1 ; CD = 3 ; the shortest distance and angle between the skew lines

AB and CD are 2 and 3

respectively. If the volume of the tetrahedron is V then find the value of (10V).

23. Let L denotes the value of 1

x 0

1 sin xlim cosx x

and U denote the value of f(0) where f(x) = x

2

0

sin(t t x)dt ,

then the value of 22UL


MATHEMATICS


24. An odd function is symmetric about the vertical line x = 1 and if r

r 0[f(1 4r)] 8

, find the numerical value

of 8f(1).

25. If |g(x) – g(y)| |x – y| x, y [2, 10], then the maximum value of 10

2

g(x)dx 8g( ) for [2, 10] is , then

find the sum of digits of

26. Let f be a real valued differentiable function on R such that f(1) = 1. If the y-intercept of the tangent at anypoint P(x, y) on the curve y = f(x) is equal to the cube of the abscissa of P, then the value of f(– 3) is equalto.........


MATHEMATICS


27. In a ABC the maximum value of 2 2 2A B Cacos bcos c cos

2 2 2a b c

can be expressed as qp

where p and

q are relatively prime positive integer. Find the value of (p + q) (symbols have usual meaning in a ABC)

28. Find the number of integer ‘x’ satisfying the inequality x x x 1 x4 3.2 4




29. A square loop is placed in an external uniform field as shown in (a). The torque acting is . Now imagine abranch is removed but still same current in rest of the branches. The new torque about c (center of square)in (b) will be :

I C

BB

I C

(a) (b)

(A) Zero (B) 34

(C) (D) 4

30. The mutual inductance of two coaxial coils of small radii at large distance x between them is proportional to:

(A) 1x

(B) 21x

(C) 31x

(D) 41x

31. In a standing wave, the phase difference at any time t, between two particles of the medium seperated by adistance x.(A) Depends on x and t (B) Depends on x but independent of t(C) Depends on t but independent of x (D) Independent of both x and t



PHYSICS


32. A block of mass m is released highest point of circular path of radious R on the smooth surface of a wedgehaving cylindrical cut as shown. If the wedge is fixed, it has a speed of 10 m/s at the bottom. If the wedge ismovable its speed at the bottom is:(C is center of cylindrical cut)

RSmoothsurface

C

m

m

(A) 5 m/s (B) 10 m/s (C) 5 2 m/s (D) 10 2 m/s

33. A particle of mass m, moving with a velocity 0 0ˆ ˆv v i v j

, elastically collides with another particle of mass

2m at rest. Mark the correct statement.

(A) The direction along which C.M. move is ˆ î j–

2

.

(B) The speed of m just before collision in C-frame is 2 v0.

(C) The speed of 2m just before collision in C-frame is 2 v0.

(D) The speed of 2m just after collision in C-frame is 02v3

.


PHYSICS


34. An ammeter should have very low resistance to ensure.(A) large deflection.(B) More heat is dissipated.(C) That it does not change the value of actual current in the circuit.(D) That ammeter draw negligible current

35. A particle is performing SHM. Magnitude of its maximum acceleration is a. Find magnitude of average

acceleration for duration of 76 time period starting from mean position.

(A) 3a

7(B)

a7 (C)

3a14 (D) None of these

36. In the arrangements shown, all the resistors are identical. Identical constant voltage (dc) sources are connectedto each of the arrangements. Write the sequence of arrangemetns in decreasing order of power consumedbetween the end points.

(I) (II)

(III) (IV)

(A) II, I, IV, III (B) III, IV, I, II (C) II, IV, I, III (D) III, I, IV, II


PHYSICS





A pistol-cylinder device contains 25 g of steam that is maintained at a constant pressure of 300 kPa. A

resistance heater within the cylinder is turned on and passes a current of 0.2A for 5 min from a 120- V

source. At the same time, a heat loss of 3.7 kJ occurs. Assume steam to behave like ideal gas.

[Take R = 253 J/mol – K]

0.2A

120V

5 min

H O2

m=25gP=300kPa

Q =3.7 kJout

37. Choose the correct statement among the following.(A) Internal energy of the steam will remain constant during this process.(B) Internal energy of the steam will decrease during this process.(C) The net heat gained by the steam is more than heat lost by the system.(D) The net heat gained by the steam is less than heat lost by the system.

38. Choose the correct statement among the following.(A) The rise in temperature of steam is 750 ºC.

(B) The increase in volume of steam is 8753 × 10–7 m3.

(C) Work done by steam on the piston is 875 J.(D) Internal energy of steam falls by 2625 J during the process.


PHYSICS


Paragraph for Question Nos. 39 to 41A convex lens, a concave mirror and a convex mirror have same magnitude of focal length are available. In thefigure shown, these are denoted as optical element E, the real object O and image (real or vitural) is denotedas I. Three points A, B and C are on a straight line as shown. AC is less than three times the focal length ofoptical element. Two trials are conducted giving results as shown. Position B is the same for both trials.

A B C

O

O

I

E I

ETrial-I

Trial-II

39. In trial-I, E can be :(A) Only a convex lens (B) Only a concave mirror(C) Only a convex mirror (D) Convex lens or a concave mirror

40. In trial-II, E is :(A) Convex lens (B) Concave mirror(C) Convex mirro (D)Both concave mirror and convex mirror are possible

41. In the case of trial-I, consider the correct element then BC (ie-image distance) can be :

(A) AC2

(B) AC2

(C) AC2

(D) none of these




Multiple Correct Choice TypeThis section contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for itsanswer, out of which ONE OR MORE is/are correct.

42. ABCD is a regular tetrahedron made of six conductors, and is moving in a region of uniform magnetic field asshown. Now choose the correct option (S) :(A) VA < VD

(B) VB = VC

(C) VD > VB

AB

B C

D

V

(D) VA > VD

here VA, VB, VC and VD represents potentials at these points.

43. Which of the following will have different time period if taken to the moon ?(A) A torsional pendulum(B) A physical pendulum(C) A spring-mass system placed vertically(D) An hourglass clock, which is essentially a vessel filled with liquid emptying through a hole in the bottom.

44. A girl stops singing a pure note. She is surprised to hear an echo of higher frequency, i.e. a higher musicalpitch then :(A) There could be some warm air between the girl and the reflecting surface.

(B) There could be two identical fixed reflecting surfaces, at separation of 2

from the girl.

(C) The girl could be moving towards a fixed reflector.(D) The reflector could be moving towards the girl.



PHYSICS45. A conducting sphere of radius R and charge Q is placed near a uniformly charged nonconducting infinitely

large thin plate having surface charge density on front surface only. (Assume that A, B, C are just inside thesphere).

++++++

O

AB

+Q

4RC

(A) The potential difference across points B and C on the sphere is 0

R .

(B) The potential difference between points B and C is zero.(C) The electric field at O due to charge on sphere is more than electric field at C due to charge on sphere.(D) Electric field at O due to charge on sphere is same as that at B.

46. A disc of mass M radius R is placed on a rough incline of angle . A force is to be applied parallel to inclineat the top most point of disc to keep it at rest.

(A) Applied force is Mgsin

2

F

(B) Friction force is Mgsin

2

(C) Minimum friction coefficient required to keep the body at rest in this situation is tan

2

(D) Minimum friction coefficient required to keep the body at rest in this situation is tan.


PHYSICS



This section contains 10 questions. The answer to each of the questions is a single-digit integer, rangingfrom 0 to 9. The appropriate bubbles below the respective question numbers in the ORS have to be darkened.For example, if the correct answers to question numbers X, Y, Z and W (say) are 6, 0, 9 and 2, respectively,then the correct darkening of bubbles will look like the following :In all cases round answer to nearest integer value (if required)

0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

47. An unknown cell balances 300 cm of wire in a potentiometer circuit, but the balance length reduces to 280cm when a resistance of 28is added in parallel with the cell. A standard cell of emf 1.1 V balances 220 cmon the same potentiometer. The balance length (in cm) when 48resistance is connected across theunknown cell is 32 K, then K is :

48. A particle starts at A with initial speed v0 = 10 m/sec. It moves along a circular path under the action of avariable force which is always directed towards B. Point A and B are end points of a diameter. Its speed(in m/sec) when it reaches P is 5n, then n is :

60º AB

P

O

10m/sec


PHYSICS


49. In the situation shown in figure ABCDE is a cylindrical container of radius 12h and height 41h. The line ofsight of the person is EP. AB is silvered. When the container is filled with a liquid of refractive index upto

height 32h point C becomes just visible via reflection then refraction. If the value of is 12N

, then find N.

A

18h

E

41h

B C D12h 12h

P

air

50. Each of the twelve wires have a resistance R ohms. The equivalent resistance of the circuit as shown in the

figure between the junctions A and B is 4

kR then K = ?.

A

B


PHYSICS


51. Two identical capacitors with charges Q0 each are connected as shown. Initial seperation between plates isd0. Now left plate of upper capacitor and right plate of lower capacitor is moved towards left with speed V in

the direction shown. The current in the circuit then can be written as N 0

0

Q Vd . Find N.

(N is an integer)

+Q0 –Q0v

+Q0 –Q0

v

52. A body of mass m = 4kg starts moving with velocity v0 in a straight line is such a way that on the body workis being done at the rate which is proportional to the square of velocity as given by P = v2 where

= 0.693

2. The time elapsed in seconds before velocity of body is doubled is :


PHYSICS


53. A square loop of side L = 1m and mass M = 0.5 kg is made up of wire of resistance R = 100 . The loop,

moving with a velocity iv0 in the horizontal x-y plane enters a region 0 < x < 2L having constant magnetic

field kT10B . Find the maximum value of v so that loop does not completely enter magnetic field.

54. A spherical soap bubble has internal pressure P0 and radius r0 and is equilibrium in an enclosure with

pressure 9P8P 0

1 . The enclosure is gradually evacuated. Assuming temperature and surface tension of

soap bubble to be fixed find the value of radiusinitialradiusfinal

of soap bubble.


PHYSICS


55. If current in the branch CD of the circuit is 8+n amperes,find n.

DA

B

C

30V

3

2 22

56. A glass capillary sealed at the upper end is of length 0.11 m and internal diameter 2 × 10–5m. The capaillarytube is immersed vertically in a liquid of density 103 kg/m3 and surface tension 5 × 10–2 N/m. The liquid wetsglass. Then length (in mm) the capillary should be immersed so that liquid level inside and outside thecapillary becomes the same is 5 N, then the value of N is :[Atmospheric pressure = 1 × 105 Pa, Acceleration due to gravity = 10 m/s2].




57. [( –C H )Mo(CO) ]55 5 3 2

[( –C H )Mo(CO) ]55 5 2 2

( )I ( )II

+ 2CO

If both compounds (I) and (II) follow EAN rule, then in the given reaction Mo–Mo bond order changes from(A) 2 to 3 (B) 2 to 4 (C) 1 to 3 (D) 1 to 4

58. The correct order of acidity of following compounds isO

O

O

O

O

O

HO

HO

(i) (ii) (iii)(A) i > ii > iii (B) ii > iii > i (C) iii > i > ii (D) iii > ii > i

59. A metal ‘X’ reacts with dil. HNO3 and produces colourless solution along with liberation of nitric oxide gas.Thus obtained colourless solution gives yellow precipitate on reaction with Na2CrO4, then metal ‘X’ is refinedby(A) Distillation (B) Liquation (C) Amalgamation (D) Vapourphase refining



CHEMISTRY


60.

OH(i) Conc. H SO , 100°C(ii) NaOH(aq), Br

2 4

2

(iii) H SO /H O, 200°C distilled2 4 2

X

X will be

(A)

OHBr

(B)

OH

Br

(C)

OH

Br

(D)

OH

Br

Br

61. Which is incorrect statement ?(A) AgBr shows Frenkel defect as well as schottky defect.(B) Density may be increase due to impurity defect.(C) End centred cubic unit cell does not exist in nature(D) Orthorhombic crystal system has three bravias lattices.

62. Which mechanism follow during acid catalysed and base catalysed hydrolysis of epoxide respectively.(A) SN1 and SN2 (B) SN2 and SN1 (C) SN1 and SN1 (D) SN2 and SN2


CHEMISTRY63. The reactive intermediate involved in the following reaction is

Br N—Me

H

NaNH2

N

Me(A) a carbocation (B) a carboanion (C) a free radial (D) an aryne

64. Which is correct statement ?(A) Absorption is always exothermic process.(B) Adsorption and absorption both are surface phenomenon.(C) Chemical adsorption is monolayer adsorption.(D) Physical adsorption is specific in nature.



CHEMISTRY





Conductometric titration is a type of titration in which electrolytic conductivity of reaction mixture is

continuously monitored as one reactent is added. The equivalence point at which the conducitivity undergoes

a sudden change.65. Which is correct graph for titration of CH3COOH Vs NH4OH ?

(A)

volume of NH OH4

conductivity

(B)

volume of NH OH4

conductivity

(C)

volume of NH OH4

conductivity

(D)

volume of NH OH4

conductivity

66. Which is correct graph for titration of NH4OH Vs HCl ?

(A)

Con

duct

ivity

volume of HCl

(B)

Co n

d uct

ivit y

volume of HCl

(C)

Con

duct

ivity

volume of HCl

(D)

Con

duct

ivity

volume of HCl


CHEMISTRY


Paragraph for Question Nos. 67 to 69A chemist has prepared new classification of cation as like present classification of cations analysis whichis used to separate cations in school laborateries. This classification is also based on the value of theirsolubility products with different anions for Ag+, Hg2

2+, Pb2+, Cu2+, Bi3+, Hg2+, Cd2+, Cr3+, Fe3+, Fe2+, Ni2+,Co2+, Mn2+, Zn2+, Mg2+, Ba2+, Sr2+, Ca2+ cations.

Group no.1234

Group cations Group reagentKI limited

KCN limitedNa CrO + CH COOH

Na C O + CH COOH2 4 3

2 2 4 3

67. Which group contains maximum number of cations.(A) Group-1 (B) Group-2 (C) Group-3 (D) Group-4

68. If limited NaOH is used in group-1 instead of limited KI solution, then which cation will precipitate in group-2.(A) Fe2+ (B) Pb2+ (C) Zn2+ (D) None of these

69. If fourth group reagent [Na2C2O4 + CH3COOH] is interchanged with third group reagent [Na2CrO4 + CH3COOH],then group number of which cation(s) is changed.(A) Ba2+ (B) Sr2+ (C) Ca2+ (D) All of these


CHEMISTRY




70. Which of them can act as oxidising agent in acidic as well as in alkaline medium.(A) KMnO4 (B) K2Cr2O7 (C) H2O2 (D) Cl2

71. Which of the following statement is true regarding fatty acids(A) Fatty acids dissolve in nonpolar salvent(B) Triglyceride are ester of fatty acids(C) Most naturally occuring fatty acids have trans double bonds(D) Fatty acids are bio synthesized from acetate

72. Consider the following thermal decomposition reactions.

x element having highest % in air

y element having highest % in earth crust

then compounds, x and y are respectively.(A) (NH4)2Cr2O7, K2Cr2O7 (B) (NH4)2CO3, K2CO3

(C) NH4MnO4, KMnO4 (D) (NH4)3PO4, K3PO4



CHEMISTRY73. In which of the following process(es) pH of the solution decreases.

(A) When CuSO4(s) is mixed with NH3(aq)

(B) When BaCO3(s) is mixed with HCl(aq)

(C) When Al(OH)3(s) is mixed with NaOH(aq)

(D) When CO2(g) is passed into Ca(OH)2 (aq.)

74. Which of following statements about azo dye coupling reaction in true?

(A) It is electrophilic substitution reaction

(B) Electron withdrawing group at Benzene diazonium salt increases the rate of reaction

(C) Electron donating group at phenol increases the rate of reaction

(D) Extended conjugate system through –N=N– bond is responsible for colour



CHEMISTRYSECTION - IV

Integer Answer TypeThis section contains 10 questions. The answer to each of the questions is a single-digit integer, rangingfrom 0 to 9. The appropriate bubbles below the respective question numbers in the ORS have to be darkened.For example, if the correct answers to question numbers X, Y, Z and W (say) are 6, 0, 9 and 2, respectively,then the correct darkening of bubbles will look like the following :In all cases round answer to nearest integer value (if required)

0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

75. X colddil KMnO4

Y HIO4 Z OH

O

HHO

Total no. of possible stereoisomers of X and Y for above reaction.

76. For compounds AgCl, AgBr, AgI, Ag2S, find the value of (P + Q – R – S).where : P = Total number of compound(s) that are soluble in conc. NH3 solution.

Q = Total number of compound(s) that are soluble in hypo solution.R = Total number of compound(s) that are soluble in KCN solution.S = Total number of compound(s) that are soluble in dil. HNO3.



CHEMISTRY77. 5 mol of sucrose in 1000 g of water undergo inversion according to pseudo first order kinetics as following.

C12H22O11 + H2O C6H12O6 + C6H12O6

glucose fructoseAfter 4 min, elevation in boiling point of solution is 3.75 K. If angle of rotation is 15º intially and after a longtime angle of rotation is –5º. Calculate time (in min) when reading of polarimeter is zero.[Given : Kb(H2O) = 0.5 K kg mol–1].

78. What is the degree of unsaturation of major product for the following reaction

CH –CH–C–OH3

HO OHeat Product

79. Find total number of oxyacid(s) which on thermal decomposition produces one of the product having lowestoxidation state of underlined atom.H3PO2, H3PO3, H3PO4, HClO, HClO2, HClO3, HClO4, HNO2, HNO3, H2SO3, H2SO4



CHEMISTRY80. How many types of colloidal systems have name aerosol, solid sol and sol ?

81. Find total number of set(s) of species x1, x2, x3 respectively which follow given reaction.

1 23xRedox reactionx x Pr oduct Redoxreaction

(i) I–(aq), Fe3+(aq), S2O32–(aq), (ii) Cu2+(aq), I–(aq), S2O3

2–(aq), (iii) Br–(aq), conc. H2SO4 , I–(aq),(iv) F2, Cl–(aq), Br–(aq), (v) Na2CO3, Br2, Sn2+(aq), (vi) NO, O2, H2O,(vii) K4Fe(CN)6, H2O2/OH–(aq), H2O2/H+(aq),(viii) Cu turning, conc. HNO3, KCN, (ix) PbO2, I–(aq), Cl–(aq).

82. CH –CH–CH –C–H3 2

HO OBase Product

What is the sum of order and molecularity for above reaction.


CHEMISTRY83. Osmotic pressure of an aqueous solution of a non electrolyte solute is 300 mm Hg at 27°C, then certain

volume of solution is diluted by adding water and temperature is raised to 54°C and osmotic pressurebecomes 300 mmHg. Find % increase in volume of solution after dilution.

84. R–NH2CHCl3KOH/

R–NC

How many moles of KOH required for 1 mole of R–NH2






CODE - ADATE : 09-10-16

B. Question paper format :9. The question paper consists of 3 parts (Physics, Chemistry and Mathematics). Each



11. Section II contains 2 paragraphs. Based upon the first paragraph, 2 multiple choicequestions and based upon the second paragraph 3 multiple choice questions have tobe answered. Each of these questions has four choices (A), (B), (C) and (D), out ofwhich only one of correct.

12. Section III contains 5 multiple choice questions. Each question has 4 choices(A), (B), (C) and (D) for its answer, out of which one or more is/are correct.

13. Section IV contains 10 questions. The answer to each of the questions is aninteger, ranging from 0 to 9. The answer will have to be appropriately bubbled in theORS as per the instructions given at the beginning of the section.

C. Marking Scheme :


15. For each question in Section-II, you will be awarded 3 marks if you have darkenonly the bubble corresponding to the correct answer and zero mark if no bubbles aredarkened. In all other cases, minus one (–1) mark will be awarded.

16. For each question in Section-III, you will be awarded 3 marks if you have darkenonly the bubble corresponding to the correct answer and zero mark if no bubbles aredarkened. No negative marks will be awarded in this Section.

17. For each question in Section-IV, you will be awarded 3 marks if you darken thebubble corresponding to the correct answer and zero mark if no bubbles is darkened.No negative marks will be awarded for in this Section.




















CODE - A


DATE : 09-10-16




1. Let f(x) be a function sayisfying f '(x) = f(x) with f(0) = 1, and g(x) satisfies f(x) + g(x) = ex(x + 1)2, then the

value of dx)x(g)x(fe1

0

x– is

(A) e (B) e – 1 (C) 2e

(D) e – 2

2. The internal angle bisector of A intersects the base BC of ABC at D. A variable line EF is drawn parallelto base BC such that points E and F are on sides AB and AC respectively. If area of ABC is 100, then themaximum value of area of DEF is :(A) 25 (B) 50 (C) 100 (D) 200

3. A line y = x + 2 is drawn on the co-ordinate plane. This line is rotated by 90º clockwise about the point (0, 2).A line y = –2x + 10 is drawn and a triangle is formed by these three lines. If the area of the triangle is , thenfind the value [] (where [k] denotes the greatest integer less than or equal to k).(A) 42 (B) 36 (C) 21 (D) None of these



MATHEMATICS


4. If the sum of all the solutions of the equation 3cot2 + 10cot + 3 = 0 in [0, 2] is p then p is equal to :(A) 5 (B) 6 (C) 4 (D) 2

5.

dx)x–1(x

1x22

2

(A) C)x(sinx–11

x–1–1ln21 21–

4

4

(B) C)x(sin

21

x–11

x–1–1ln21 21–

4

4

(C) C)x(sin21

x–11

x–1–1ln41 21–

4

4

(D) C)x(sin

21

x–11

x–1–1ln 21–4

4

6. If the ratio of 6th term from beginning and 6th term from end in the expansion of

15

23

x2x

is

24324

, then

the value of x is equal to

(A) (3)1/2 (B) 5/1

32

(C) 3/1

52–

(D) (–5)1/3


MATHEMATICS





Let f : R R be defined by f(x) = 2

2

1 px x1 px x , where p (0, 2) and g(x) = f(x) for all x R.

7.2

2

ln(f(x) | sinx |)dx

is equal to

(A) 0 (B) 1

4 ln4

(C) 1

2 ln8

(D) 1

ln16

8. Let xe

20

g(t)(x) dt

1 t

, then

(A) (x) is strictly increasing function (B) (x) has local maxima at x = 0(C) (x) has local minima at x = 0 (D) (x) is strictly decreasing function

9.3 2

ln f(x)3

(x 1)dx(1 2 )

is equal to

(A) 0 (B) 3 (C) 6 (D) 12


MATHEMATICS



Let 1 0 0

A 2 1 03 2 1

and R1, R2, R3 be the row matrices. Satisfying the relations, R1 A = [1 0 0],

R2A = [2 3 0] and R3A = [2 3 1]. If B is square matrix of order 3 with rows R1, R2, R3 in order, then

10. The value of det(B) =(A) – 3 (B) 0 (C) 1 (D) 3

11. The value of det(2A100B3 – A99B4) is equal to(A) – 100 (B) – 27 (C) 27 (D) 100

12. Sum of all elements of matrix B–1 is equal to(A) 0 (B) 5 (C) 8 (D) 10


MATHEMATICS





P Q R S

P

P

P

Q

Q

Q

R

R

R

S

S

S

A

B

C

D

P Q R ST

T

T

T

T

13. Column-I Column-II(A) The roots of the equation z4 + z3 + z + 1 = 0 (P) Parallelogram

on the complex plane are represented by the vertices of

(B) If variable complex number ‘z’ satisfy the condition (Q) Square

z z z z 4 , then locus of z is given by

(C) Th roots of the equation z4 + z3 + z2 + z + 1 = 0 (R) Isosceles trapezium

on the complex plane are represented

(D) The roots of the equation z6 + z4 – z2 – 1 = 0 (S) Trapezium which is not isosceles

on the complex plane are represented

(T) Equilateral triangle


MATHEMATICS


14. Let the points A, B, C and D form a regular tetrahedron ABCD in 3-diamensional space where the edge length

of the tetrahedron is 2 , then

Column-I Column-II

(A) The angle between any two faces of ABCD is (P) 1 1cos

3

(B) The angle between any edge and face not containing that edge is (Q) 1tan 2 3

(C) The angle between two opposite edges of the tetrahedron ABCD is (R) 1 1cos2

(D) The volume of the tetrahedron ABCD is more than (S) 1 5 1sin

4

(T) sin–11



MATHEMATICSSECTION - IV


0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

15. If a line with positive slope passing through point P(0, 1) intersects the curve y = x2 – x at A and B such that(PA) (PB) = 2, then AB is equal to

16. If the equation x2 – 4x – (3k – 1) |x – 2| – 2k + 8 = 0, k R, has exactly three distinct solutions, then k isequal to



MATHEMATICS

17. Let f(x) = ||x – 2| – 1| – 1 and

0x,|)x|(sgnsin0x,))xsgn(1(tan0x,))x(sgn(–cos

)x(g1–

1–

1–

.

Then the largest integral value of x for which (gof)(x) = 0 is

18. Let dx)}x{}x{1(e9

0

2x and dx)}x{}x{1(eJ1

0

2x . If ne – 1

J e – 1 , then n is equal to

(where {·} denotes fractional part function)

19. The diameter of circle whose normal at the point (–3, 4) cuts the circle again at point common to the line

7x + y = 0 and circle 07y–x–yx 22 is




20. A stream of water of density , cross-sectional area A, and speed v strikes a wall that is perpendicular to thedirection of the stream, as shown in the figure. The water then flows sideways across the wall. The forceexerted by the stream on the wall is

v

(A) v2A (B) vA/w (C) ghA (D) v2A/

21. Two factories are sounding their sirens at 800 Hz. A man goes from one factory to other at a speed of1 m/s. The velocity of sound is 320 m/s. The number of beats heard by the person in one second will be:(A) 8 (B) 4 (C) 5 (D) 2

22. A 4 g bullet is fired horizontally with a speed of 300 m/s into 0.8 kg block of wood at rest on a table. Bulletgets embedded in it. If the coefficient of friction between the block and the table is 0.3, how far will beblock + bullet slide approximately :(A) 0.758 m (B) 0.19 m (C) 0.569 m (D) 0.379 m



PHYSICS


23. The circuit shown here has two batteries of 8.0 V and 16.0 V and three resistors 3, 9 and 9 and acapacitor 5.0 µF :

5µF3 9

8.0 V 16.0 V

I1 I2

I

9

How much is the current I in the circuit in steady state ?(A) 1.6 A (B) 2.5 A (C) 0.67 A (D) 0.25 A

24. When body X is said to be at higher temperature than body Y, this means that :(A) body X has more energy than body Y(B) body X is heavier than body Y(C) body X loses heat energy faster than body Y(D) body X loses heat energy to body Y when they are in contact

25. A cone of base radius R and height h is located in a uniform electric field E

parallel to its base. The electric

flux entering the cone is :

(A) 4EhR (B) 1EhR2

(C) EhR (D) 2EhR


PHYSICS




Paragraph for Question Nos. 26 to 28A chair shaped frame PORSTUP is kept on frictionless horizontal table with QRST as horizontal and TUPQvertical. The frame has uniform linear mass density and length of each straight part is L.

A current I is flown, the coil having direction P to Q. An external magnetic field 0B B i is applied.

Uy

L

P

L

LT L S x

LRLQ

26. Find the minimum value of magnetic field B = B0 so that toppling begins

(A) B0 = 2 g

I(B) B0 =

3 gI

(C) B0 =5 g

I(D) B0 =

g2

I

27. Suppose topling begins at this value of field. What will be the displacement of line QT till QPUT becomehorizontal

(A) 2L3 (B)

L2

(C) 0 (D) none of these

28. If there is sufficient friction betwen frame and table to avoid sliding then with what angular velocity framestrikes the plane during first collision. Neglect induction effect.

(A) BL

I(B)

6 B5 L

I(C)

12 B5 L

I(D) none of these


PHYSICSParagraph for Question Nos. 29 to 31

In the situation shown in figure current AC is 2A along A to C and 1A in AE, from A to E. If the polarity ofbattery is reversed current in BC becomes 1A along B to C. Battery has no internal resistance.

D

B

C

A Y

1 2

12X

XY

E

29. The emf of battery will be(A) 1 volt (B) 2 volt (C) 3 volt (D) 4 volt

30. The value of equivalent resistance of circuit will be(A) 1 (B) 2 (C) 3 (D) 4

31. Y-X is equal to(A) 1 (B) 2 (C) 3 (D) 4



PHYSICS





P Q R S

P

P

P

Q

Q

Q

R

R

R

S

S

S

A

B

C

D

P Q R ST

T

T

T

T

32. A particle of mass 1kg is at (0, –1m). It’s initial velocity is i m/s. A force acting on the particle is given by

F xi ky j where (x, y) is position coordinate of particle in meter and force in newton. Match for the

trajectory for different value of k.Column-I Column-II

(A) k = 0 (P) Straight line segment(B) k = 1 (Q) Circle(C) k = 4 (R) Segment of parabola(D) k = –1 (S) y coordinate unbounded

(T) x coordinate bounded


PHYSICS


33. Two transparent media of refractive indices 1 and 2 have a solid lens shaped transparent material of refractiveindex 2 between them as shown in figures in Column-II. A ray traversing these media is also shown in thefigures. In column-I different relationships between 1, 2 and 3 are given. Match them to the ray diagramshown in Column-II.

Column-I Column-II

(A) 1 < 2 (P) 2 13

(B) 1 > 2 (Q) 2 13

(C) 2 = 3 (R)2

13

(D) 2 > 3 (S)

213

(T)2

13


PHYSICS




0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

34. Two highly conducting long cylinders of cross sectional area A = 10–3 m2 are fitted smoothly together (figure)having internal air pressure P0 = 105 Pa. Masses M are hung from cables attached to each of the cylinders.In equilibrium X becomes double.Then M is (in kg) (Take g = 10 m/s2 and process to be isothermal)

M M

x


PHYSICS


35. A monoatomic gas follows a cyclic process ABCA as shown here. If the heat given to the gas during processAB is 100J, the heat extracted (in joules) from the gas during process CA is 5n then n is :

PB

CA

V0 4V0

36. On a rough horizontal surface a block is kept as shown. If the horizontal force applied on the block is lessthan 40 N, the block does not slide. If instead of the block we take a 10 kg sphere and pull it horizontalloy atits center, the maximum force (in N) that we can apply so that the sphere does not slide is 70 K then K is :

10 kg F



PHYSICS37. When Q amount if heat is given to an ideal diatomic gas in a process, it performs KQ work on it surroundings.

Find the molar heat capacity (in SI units) of the gas for the process is (15 x) R then the value of x is :[Take : K = 23/24, R = 25/3 J/mol-K]

38. In a magnetic field from a high altitude drops a ring, having diameter d and resistance r. The plane of the ringis hrizontal at all the time. The terminal velocity of the ring (in m/s) is 32 K, find K, where the magnetic fieldvaries with altitude according to B = B0 . (1 + ah). The mass of the ring in m.[Take : m = 10 gm, R = 10, d = 10 cm, B0 = 1 T, a = 10 m–1].




39. In a hypothetical solid, "C" atoms forming cubical closed packed lattice. "A" atoms occupy all tetrahedralvoid and "B" atoms occupy all octahedral voids. There is no distortion in ccp lattice. Fraction of bodydiagonal not covered up by atoms is :(A) 0.76 (B) 0.24 (C) 0.68 (D) None of these

40. How many grams of sucrose (molecular weight = 342) should be dissolved in 100g water in order to producea solution with a 105°C difference between the freezing point and the boiling point temperature?(Kf = 1.86 K–Kg/mole, Kb = 0.51 K–Kg/mole)(A) 34.2 g (B) 72.15 g (C) 342 g (D) 460 g

41. Na2S2O3 + dil. HCl warm NaCl + X(g) + residueWhiteY

gas ‘X’ does not undergoes redox reaction with

(A) Fe3+(aq) (B) 3IO (aq) H (aq) (C) I–(aq) (D) Cl2 (g)



CHEMISTRY


42. 0 2 1 1eq 2(BaCl ) 160 cm eq ohm

0 2 1 1eq 3 4(K PO ) 140 cm eq ohm

0 2 1 1eq(KCl) 100 cm eq ohm

The value of Ksp of Ba3(PO4)2 is :[Given : Ba3(PO4)2 is a sparingly soluble salt, conductivity of Ba3(PO4)2 K = 12 × 10–6 ohm–1 cm–1](A) 2 × 10–25 (B) 1.08 × 10–38 (C) 1.08 × 10–23 (D) None of these

43. Select the correct pair of product and most acidic hydrogen in the reactant for given reaction.

O

H3C14

KOCl

60°C ProductH3C

14

(A) CHCl3 & (B) CHCl3 & (C) 14CHCl3 & (D) 14CHCl3 &

44. A sample of ozonised oxygen diffuses 2 times faster than pure SO3 gas under identical conditions. Themass percent of O3 in the sample of ozonised oxygen is(A) 60 (B) 50 (C) 40 (D) 30


CHEMISTRY





C H7 12(i) Hot acidic/KMnO4 Y + 3CO + 2H O2 2

OH Z(X) (ii) , Heat

X is optically active and non cyclic

45. No. of chiral carbon in X(A) 1 (B) 2 (C) 3 (D) 4

46. No. of alpha hydrogen in Y(A) 4 (B) 5 (C) 6 (D) 2

47. No. of possible products Z (Excluding stereoisomer)(A) 2 (B) 4 (C) 3 (D) 1


CHEMISTRY


Paragraph for Question Nos. 48 to 50When 100 ml 1N H2SO4 was mixed with 100 ml 1.0 M NaOH in a solution calorimeter, a temperatureincrease of 2.85 K was observed and this experiment-1 is used to measure the heat capacity ofcalorimeter as enthalpy of neutralisation of strong acid and strong base is –57 kJ mol–1. In a secondexperiment, 100 ml 2M NH4OH (Kb = 10–5) was mixed with 100 ml 1N H2SO4 (under identical condition toexperiment-1) where a temperature rise of 2.75 K was observed.[Given : heat capacity of solution = 4.2 J g–1 K–1 density of all solution = 1g/ml, log 4 = 0.6, pKw = 13]

48. Heat capacity of solution calorimeter is (in kJ K–1).(A) 2 (B) 1.16 (C) 2.84 (D) 1.76

49. Enthalpy of dissociation of NH4OH is (kJ mol–1)(A) 1 (B) 2 (C) 3 (D) 4

50. pH of solution in experiment 2 is :(A) 7.7 (B) 8 (C) 8.7 (D) 9


CHEMISTRY





P Q R S

P

P

P

Q

Q

Q

R

R

R

S

S

S

A

B

C

D

P Q R ST

T

T

T

T


(Aqueous solution of Salt) (Reagents)

(A) Fe2(SO4)3 (P) Formation of complex ion with excess Na2S2O3

(B) CuSO4 (Q) Formation of precipitate of basic carbonate with Na2CO3

(C) Hg(NO3)2 (R) Formation of precipitate with (NH4)2S in non-redox reaction

(D) AgF (S) Redox reaction with KI

(T) Formation of precipitate with BaCl2


CHEMISTRY



(A) CH —C–H3

O(P) Disproportionation reaction

(B) H–C–H

O(Q) Condensation reaction

(C) CH —C–CH3 3

O(R) Ammoniacal silver nitrate solution

(D) C—H

O

(S) Cl + OH2

(T) Elimination reaction


CHEMISTRY




0X

1

2

3

4

5

6

7

8

9

0 0 0Y Z W

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

53. Find out total number of moles of white phosphorus required to produce six moles of sodium hypophosphitefrom reaction between white phosphorus and NaOH solution at required temperature.

54. 24 mol carbon reacts with 18 mol of O2 to form CO and CO2. Calculate the density (in g/) of reaction mixtureat 360 K temperature and 1.642 atm pressure.



CHEMISTRY

55. Consider hydrolysis of H2S2O8 : H2S2O8 + H2O .T.R P + Q

Where, compound ‘P’ has ‘open book’ like structure, then find out value of |x – y|.Where, x = maximum number of atom(s) that can lie in a plane of a molecule of H2S2O8 = 5.

y = Maximum number of oxygen atom(s) that can lie in a plane of a molecule of ‘Q’ = 3.

56. Following reaction takes place at 600

2.303 0.8314 K temperature.

H2(g) + 2Ag+(aq) 2Ag(s) + 2H+(aq)

2HP = 1.0 bar, [Ag+] = 10–6 M, [H+] = 10–3 M , fGº(Ag+,aq) = 75 kJ mol–1

Calculate z.

where z = r| G(in kJ) |19

57. If latent heat of fusion of ice is being used in breaking only x% of hydrogen bonds in ice andH0 of H-bonding is 12 kcal/mol. What is the value of x?[Given : Latent heat of fusion of ice = 80 cal/g.K]





CODE - A

B. Question paper format :9. The question paper consists of 3 parts (Physics, Chemistry and Mathematics). Each



11. Section II contains 2 groups of questions. Each groups has 3 questions based on aparagraph. Each question has 4 choices (A), (B), (C) and (D) for its answer, out ofwhich only one of correct.

12. Section III contains 2 questions. Each questions has four statements (A, B, C and D)given in Column I and five statements (P, Q, R, S and T) in Column II. Any givenstatement in Column I can have correct matching with one or more statement(s)given in Column II. For example, if for a given question, statement B matches with thestatements given in Q and R, then for that particular question, against statement B,darken the bubbles corresponding to Q and R in the ORS.

13. Section IV contains 5 questions. The answer to each of the questions is aninteger, ranging from 0 to 9. The answer will have to be appropriately bubbled in theORS as per the instructions given at the beginning of the section.

C. Marking Scheme :

14. For each question in Section I, you will be awarded 5 marks if you darken thebubble corresponding to the correct answer and zero mark if no bubble is darkened.In case of bubbling of incorrect answer, minus two (–2) mark will be awarded.

15. For each question in Section II, you will be awarded 3 marks if you darken thebubble corresponding to the correct answer and zero mark if no bubble is darkened.In case of bubbling of incorrect answer, minus one (–1) mark will be awarded.

16. For each question in Section III, you will be awarded 2 marks for each row inwhich you have darkened the bubble(s) corresponding to the correct answer. Thus,each question in this section carries a maximum of 8 marks. There is no negativemarking for incorrect answer(s) for this section.

17. For each question in Section IV, you will be awarded 3 marks if you darkened thebubble corresponding to the correct answer, and zero mark if no bubble is darkened.There is no negative marking for incorrect answer(s) for this section.

DATE : 09-10-16

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DATE : 24-04-16 VIBRANT ACADEMY